https://fizipedia.bme.hu:80/index.php?title=TLS_noise&feed=atom&action=historyTLS noise - Laptörténet2024-03-29T07:44:52ZAz oldal laptörténete a wikibenMediaWiki 1.21.1https://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23792&oldid=prevHalbritt, 2018. november 16., 12:55-n2018-11-16T12:55:47Z<p></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:55-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">14. sor:</td>
<td colspan="2" class="diff-lineno">14. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tilde{C}$ is $??C$ using our orifice geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $90^\circ$ opening angle.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tilde{C}$ is $??C$ using our orifice geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $90^\circ$ opening angle.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The $R_\textrm{M}$ dependence of the CNR predicted by this simple model calculation clearly follows the experimentally observed trends both in the ballistic and in the diffusive limit. Here we emphasize, that in both limits $>99??\%$ of the CNR stems from the $\left|\underline{\textbf{r}}\right|<2a$ region, i.e. the small junction acts as a magnifier for the processes happening in the junction neighborhood, and suppressing the further processes. This is in sharp contrast to the original nanobridge geometry of the electromigrated Ag wires, where all the TLSs within the nanobrige give relevant contribution to the noise. </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Whereas our model includes numerous simplifications yielding uncertain prefactors, still as a validation we use this model as a fitting curve such that the experimental data are fitted with the diffusive/ballistic limit bellow/above the crossing point of the ballistic and diffusiv power law lines on the log-log plot. Using $k_F=???$ [hivatkozás] and the $90^\circ$ opening angle geometry the least square fitting of our data yields $l=??$ and $C\cdot\sqrt{\rho_\textrm{TLS}}=??$. Ezt majd az eredményeket látva diszkutáljuk.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in [Fredicikk]. Following Ref. [Fredicikk] we will refer such dynamical defects as two levele systems (TLSs), but actually these diffects may also fluctuate between more than two different structural arrangements, the main ingradient is that the scattering on thses defects varies with time. First we emphasize, that a point-contact, i.e. a small, nanometer-scale junction between macroscopic electrodes always acts as a magnifier</del>, i.e. all the scattering processes happening in the vicinity of the junction have highly enhanced influance on the conductance, and therefore it is even possible to observe the temporal conductance fluctuations due to a single two level system [Ralph, Caro, Kaijsers]. On the other hand the processes happening far away from the junction have highly suppressed contribution to the conductance. For the sake of simplicity we model an orifice like point contact, i.e. an orifice with diameter d in an infinite isolating plane between two conducting electrodes (see Figure). Without any scattering in the junction region, this orifice like \emph{ballistic} point contact has a conductance of [Fredicikk]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">    </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">== == </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>, i.e. all the scattering processes happening in the vicinity of the junction have highly enhanced influance on the conductance, and therefore it is even possible to observe the temporal conductance fluctuations due to a single two level system [Ralph, Caro, Kaijsers]. On the other hand the processes happening far away from the junction have highly suppressed contribution to the conductance. For the sake of simplicity we model an orifice like point contact, i.e. an orifice with diameter d in an infinite isolating plane between two conducting electrodes (see Figure). Without any scattering in the junction region, this orifice like \emph{ballistic} point contact has a conductance of [Fredicikk]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$G_\textrm{ballistic}=\frac{2e^2}{h}M,\  M=\left(\frac{k_\textrm{F}a}{2}\right)^2,$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$G_\textrm{ballistic}=\frac{2e^2}{h}M,\  M=\left(\frac{k_\textrm{F}a}{2}\right)^2,$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>where M is the number of open conductance channels in the contact, $a$ is the radius of the contact, $k_\textrm{F}$ is the Fermi wavenumber, and $G_0=2e^2/h$ is the quantum conductance unit. If a TLS is placed to the center of the orifice, i.e. an atom or a group of atoms can fluctuate between two or more metastable positions,  the electrons will scatter on the TLS modifying the above ballistic conductance formula (see Fig.? a, red lines). If we consider the scattering on a  single atom-sized structural defect, the correction of the conductance to the above formula is on the order of the quantum conductance unit, or smaller. This conductance correction may differ in the various states of the TLS (see the solid and the dotted line after the scatterring on the TLS in Fig.?), introducing a temporal conductance variation, $\Delta G_\textrm{ballistic}=(2e^2/h)C$. Here C defines the amplitude the temporal conductance variation in the units of $G_0$ for a single TLS positioned in the center of a ballistic point contact within the bandwidth of the measurement. Based on earlier studies, the reasonable values of C are at the range of the fractions of $G_0$, like $C\approx 0.01-0.1$ [????]. If the TLS is placed further away from the contact, the fluctuation of the conductance decreases with a geometrical factor $K_\textrm{ballistic}$, $\Delta G_\textrm{ballistic}=G_0\cdot C \cdot K_\textrm{ballistic}$. According to the detailed calculations in Ref. [Fredicikk] this geometrical factor scales with the square of the solid angle, $\Omega(\underline{\textbf{r}})$ at witch the orifice is seen from the position of the TLS, $\underline{\textbf{r}}$. Simply speaking, the scattering on the TLS only modifies the conductance, if the electron passing through the contact arrives to the TLS, and after that it is scattered back through the contact (see figure), where both the arrival to the TLS and the scattering back through the contact scales with $\Omega(\underline{\textbf{r}})$.  Following these considerations we use a simplified approximation for $K_\textrm{</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>where M is the number of open conductance channels in the contact, $a$ is the radius of the contact, $k_\textrm{F}$ is the Fermi wavenumber, and $G_0=2e^2/h$ is the quantum conductance unit. If a TLS is placed to the center of the orifice, i.e. an atom or a group of atoms can fluctuate between two or more metastable positions,  the electrons will scatter on the TLS modifying the above ballistic conductance formula (see Fig.? a, red lines). If we consider the scattering on a  single atom-sized structural defect, the correction of the conductance to the above formula is on the order of the quantum conductance unit, or smaller. This conductance correction may differ in the various states of the TLS (see the solid and the dotted line after the scatterring on the TLS in Fig.?), introducing a temporal conductance variation, $\Delta G_\textrm{ballistic}=(2e^2/h)C$. Here C defines the amplitude the temporal conductance variation in the units of $G_0$ for a single TLS positioned in the center of a ballistic point contact within the bandwidth of the measurement. Based on earlier studies, the reasonable values of C are at the range of the fractions of $G_0$, like $C\approx 0.01-0.1$ [????]. If the TLS is placed further away from the contact, the fluctuation of the conductance decreases with a geometrical factor $K_\textrm{ballistic}$, $\Delta G_\textrm{ballistic}=G_0\cdot C \cdot K_\textrm{ballistic}$. According to the detailed calculations in Ref. [Fredicikk] this geometrical factor scales with the square of the solid angle, $\Omega(\underline{\textbf{r}})$ at witch the orifice is seen from the position of the TLS, $\underline{\textbf{r}}$. Simply speaking, the scattering on the TLS only modifies the conductance, if the electron passing through the contact arrives to the TLS, and after that it is scattered back through the contact (see figure), where both the arrival to the TLS and the scattering back through the contact scales with $\Omega(\underline{\textbf{r}})$.  Following these considerations we use a simplified approximation for $K_\textrm{</div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23791&oldid=prevHalbritt, 2018. november 16., 12:38-n2018-11-16T12:38:15Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:38-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">10. sor:</td>
<td colspan="2" class="diff-lineno">10. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=G_\textrm{ballistic}\cdot 8l/(3\pi a)$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. 167 in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}\cdot l^2/a^2$ reduction of the geometrical factor. From these   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=G_\textrm{ballistic}\cdot 8l/(3\pi a)$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. 167 in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}\cdot l^2/a^2$ reduction of the geometrical factor. From these   </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C}_\textrm{diffusive} k_\textrm{F}l^\frac{5}{2}<del class="diffchange diffchange-inline">\ </del>\sqrt{\rho_\textrm{TLS}}left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C}_\textrm{diffusive} k_\textrm{F} l^\frac{5}{2} \sqrt{\rho_\textrm{TLS}}<ins class="diffchange diffchange-inline">\</ins>left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows, giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows, giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Here the $\<del class="diffchange diffchange-inline">tildeb</del>{C}$ is $??C$ using our orifice geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $90^\circ$ opening angle.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Here the $\<ins class="diffchange diffchange-inline">tilde</ins>{C}$ is $??C$ using our orifice geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $90^\circ$ opening angle.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23790&oldid=prevHalbritt, 2018. november 16., 12:36-n2018-11-16T12:36:28Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:36-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">10. sor:</td>
<td colspan="2" class="diff-lineno">10. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=G_\textrm{ballistic}\cdot 8l/(3\pi a)$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. 167 in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}\cdot l^2/a^2$ reduction of the geometrical factor. From these   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=G_\textrm{ballistic}\cdot 8l/(3\pi a)$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. 167 in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}\cdot l^2/a^2$ reduction of the geometrical factor. From these   </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C}_\textrm{diffusive} k_\textrm{F<del class="diffchange diffchange-inline">} \sqrt{\rho_\textrm{TLS}</del>}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C}_\textrm{diffusive} k_\textrm{F}l^\frac{5}{2}\ <ins class="diffchange diffchange-inline">\sqrt{\rho_\textrm{TLS}}</ins>left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>follows<ins class="diffchange diffchange-inline">, </ins>giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tildeb{C}$ is $??C$ using our <del class="diffchange diffchange-inline">model </del>geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $<del class="diffchange diffchange-inline">??</del>$ opening angle.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tildeb{C}$ is $??C$ using our <ins class="diffchange diffchange-inline">orifice </ins>geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $<ins class="diffchange diffchange-inline">90^\circ</ins>$ opening angle.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23789&oldid=prevHalbritt, 2018. november 16., 12:34-n2018-11-16T12:34:24Z<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:34-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">10. sor:</td>
<td colspan="2" class="diff-lineno">10. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=G_\textrm{ballistic}\cdot 8l/(3\pi a)$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. 167 in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}\cdot l^2/a^2$ reduction of the geometrical factor. From these   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=G_\textrm{ballistic}\cdot 8l/(3\pi a)$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. 167 in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}\cdot l^2/a^2$ reduction of the geometrical factor. From these   </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}<del class="diffchange diffchange-inline">$$</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{<ins class="diffchange diffchange-inline">C}_</ins>\textrm{diffusive} k_\textrm{F} \sqrt{\rho_\textrm{TLS<ins class="diffchange diffchange-inline">}</ins>}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">$$</del>=\tilde{<del class="diffchange diffchange-inline">C_</del>\textrm{diffusive<del class="diffchange diffchange-inline">}</del>}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tildeb{C}$ is $??C$ using our model geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $??$ opening angle.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tildeb{C}$ is $??C$ using our model geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $??$ opening angle.</div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23788&oldid=prevHalbritt, 2018. november 16., 12:33-n2018-11-16T12:33:12Z<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:33-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">9. sor:</td>
<td colspan="2" class="diff-lineno">9. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law $R_\textrm{M}$ dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $90^\circ$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law $R_\textrm{M}$ dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $90^\circ$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\<del class="diffchange diffchange-inline">frac</del>{8l<del class="diffchange diffchange-inline">}{</del>3\pi a<del class="diffchange diffchange-inline">}G_\textrm{ballistic}</del>$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. <del class="diffchange diffchange-inline">?? </del>in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=<del class="diffchange diffchange-inline">\frac{l^2}{a^2}</del>K(\underline{\textbf{r}})_\textrm{ballistic}$ <del class="diffchange diffchange-inline">(eq. 167 in Fredicikk)</del>. From these   </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=<ins class="diffchange diffchange-inline">G_</ins>\<ins class="diffchange diffchange-inline">textrm</ins>{<ins class="diffchange diffchange-inline">ballistic}\cdot </ins>8l<ins class="diffchange diffchange-inline">/(</ins>3\pi a<ins class="diffchange diffchange-inline">)</ins>$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. <ins class="diffchange diffchange-inline">167 </ins>in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=K(\underline{\textbf{r}})_\textrm{ballistic}<ins class="diffchange diffchange-inline">\cdot l^2/a^2</ins>$ <ins class="diffchange diffchange-inline">reduction of the geometrical factor</ins>. From these   </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C_\textrm{diffusive}}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">$$</ins>=\tilde{C_\textrm{diffusive}}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tildeb{C}$ is $??C$ using our model geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $??$ opening angle.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Here the $\tildeb{C}$ is $??C$ using our model geometry, and we estimate $\tilde{C}\approx ??C$ in a junction with $??$ opening angle.</div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23787&oldid=prevHalbritt, 2018. november 16., 12:29-n2018-11-16T12:29:23Z<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:29-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">7. sor:</td>
<td colspan="2" class="diff-lineno">7. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a constant $K=K_0$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$. The latter is the asymptotic dependence of $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk), whereas $K_0=??$ approximates the small distance limit of the same equation. The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform $C$ for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a constant $K=K_0$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$. The latter is the asymptotic dependence of $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk), whereas $K_0=??$ approximates the small distance limit of the same equation. The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform $C$ for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law $R_\textrm{M}$ dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $<del class="diffchange diffchange-inline">???</del>$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law $R_\textrm{M}$ dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $<ins class="diffchange diffchange-inline">90^\circ</ins>$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$ (eq. 167 in Fredicikk). From these   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$ (eq. 167 in Fredicikk). From these   </div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23786&oldid=prevHalbritt, 2018. november 16., 12:28-n2018-11-16T12:28:04Z<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:28-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">5. sor:</td>
<td colspan="2" class="diff-lineno">5. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively).  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively).  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a constant $K=K_0$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$. The latter is the asymptotic dependence of $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk), whereas $K_0=??$ approximates the small distance limit of the same equation. The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a constant $K=K_0$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$. The latter is the asymptotic dependence of $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk), whereas $K_0=??$ approximates the small distance limit of the same equation. The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform <ins class="diffchange diffchange-inline">$</ins>C<ins class="diffchange diffchange-inline">$ </ins>for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law <del class="diffchange diffchange-inline">junction resistance </del>dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law <ins class="diffchange diffchange-inline">$R_\textrm{M}$ </ins>dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$ (eq. 167 in Fredicikk). From these   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin formula is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq. 36 in Fredicikk], $\sigma$ being the conductivity. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$ (eq. 167 in Fredicikk). From these   </div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23785&oldid=prevHalbritt, 2018. november 16., 12:25-n2018-11-16T12:25:33Z<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 12:25-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">5. sor:</td>
<td colspan="2" class="diff-lineno">5. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively).  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively).  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a <del class="diffchange diffchange-inline">normalized value of </del>$K=<del class="diffchange diffchange-inline">1</del>$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$<del class="diffchange diffchange-inline">, which </del>is the asymptotic dependence of <del class="diffchange diffchange-inline">the normalized </del>$K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk). The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a <ins class="diffchange diffchange-inline">constant </ins>$K=<ins class="diffchange diffchange-inline">K_0</ins>$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$<ins class="diffchange diffchange-inline">. The latter </ins>is the asymptotic dependence of $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk)<ins class="diffchange diffchange-inline">, whereas $K_0=??$ approximates the small distance limit of the same equation</ins>. The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law junction resistance dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law junction resistance dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23784&oldid=prevHalbritt, 2018. november 16., 11:14-n2018-11-16T11:14:31Z<p></p>
<table class='diff diff-contentalign-left'>
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<col class='diff-marker' />
<col class='diff-content' />
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<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 11:14-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">3. sor:</td>
<td colspan="2" class="diff-lineno">3. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[file:Ballistic_diffusive.png|600px]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[file:Ballistic_diffusive.png|600px]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively). In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a normalized value of $K=1$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$, which is the asymptotic dependence of the normalized $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk). The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively).  </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a normalized value of $K=1$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$, which is the asymptotic dependence of the normalized $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk). The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law junction resistance dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The corresponding power law junction resistance dependence with an exponent of $1/4$ is demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???\cdot C$ for the orifice-like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin <del class="diffchange diffchange-inline">conductance </del>is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq <del class="diffchange diffchange-inline">?? </del>in Fredicikk]. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$. From these   </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin <ins class="diffchange diffchange-inline">formula </ins>is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq<ins class="diffchange diffchange-inline">. 36 </ins>in Fredicikk]<ins class="diffchange diffchange-inline">, $\sigma$ being the conductivity</ins>. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$ <ins class="diffchange diffchange-inline">(eq. 167 in Fredicikk)</ins>. From these   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C_\textrm{diffusive}}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C_\textrm{diffusive}}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>follows giving a power law exponent of $3/2$ in the diffusice limit, as demonstrated by the red dashed line in Fig.4b.</div></td></tr>
</table>Halbritthttps://fizipedia.bme.hu/index.php?title=TLS_noise&diff=23783&oldid=prevHalbritt, 2018. november 16., 11:10-n2018-11-16T11:10:03Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2018. november 16., 11:10-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">4. sor:</td>
<td colspan="2" class="diff-lineno">4. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively). In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a normalized value of $K=1$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$, which is the asymptotic dependence of the normalized $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk). The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Next, we model the temporal fluctuations of the conductance based on the scattering on dynamical defects in a point contact geometry following the theoretical models summarized in a previous review paper of one of the authors, [Fredicikk]. We consider both the ballistic and the diffusive limit, i.e. junctions with diameter smaller or larger than the mean free path of the electrons, $l$ (see Fig.?a and b respectively). In the ballistic limit the conductance of an orifice-like point-contact is given by the Sharvin formula, $G_\textrm{ballistic}=G_0k^2_\textrm{F}a^2/2,$ $a$ being the contact radius, $k_F$ the Fermi wavenumber and $G_0=2e^2/h$ the conductance quantum. Once an electron scatters on a dynamical defect (or two level system, TLS) close to the junction, this conductance is perturbed, and having different perturbation in the different states of the defect, a conductance noise is introduced. We model this conductance noise as $\Delta G_\textrm{ballistic}=G_0\cdot C\cdot K_\textrm{ballistic}(\underline{\textbf{r}}),$ where C defines the amplitude of the temporal conductance fluctuation within the bandwidth of the measurement for a TLS positioned in the center of the ballistic contact, whereas $K_\textrm{ballistic}(\underline{\textbf{r}})$ accounts for the variation of this conductance noise with the position of the TLS. In our simplified model we take a normalized value of $K=1$ close to the contact ($\left|\underline{\textbf{r}}\right|<a$), and $K=a^4/r^4$ if $\left|\underline{\textbf{r}}\right|>a$, which is the asymptotic dependence of the normalized $K$ along the contact axis scaling with the square of the solid angle at which the contact is seen from the TLS position (see eq. 99 in Ref. Fredicikk). The effect of multiple TLSs is modeled with a constant TLS density, $\rho_\textrm{TLS}$ using uniform C for all TLSs. Considering the contribution of the different TLSs being independent of each other $(\Delta G)^2$ is additive, and is easily integrated for the entire space yielding a normalized conductance noise of</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}<del class="diffchange diffchange-inline">,</del>$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{ballistic}=\left(\frac{\Delta I}{I} \right)_\textrm{ballistic}=\tilde{C}_\textrm{ballistic} \sqrt{\frac{\rho_\textrm{TLS}}{k^3_\textrm{F}}}\left(R_\textrm{M}G_0 \right)^\frac{1}{4}<ins class="diffchange diffchange-inline">.</ins>$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">yielding a </del>power law <del class="diffchange diffchange-inline">dependence from the </del>junction resistance <del class="diffchange diffchange-inline">$R_M$ </del>with an exponent of $1/4$<del class="diffchange diffchange-inline">, as </del>demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???C$ for the orifice like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The corresponding </ins>power law junction resistance <ins class="diffchange diffchange-inline">dependence </ins>with an exponent of $1/4$ <ins class="diffchange diffchange-inline">is </ins>demonstrated by the blue dashed line in Fig.4b. Here the $\tilde{C}$ prefactor is $???<ins class="diffchange diffchange-inline">\cdot </ins>C$ for the orifice<ins class="diffchange diffchange-inline">-</ins>like junction geometry of our model, whereas for a  more realistice Ag nanowire junction with $???$ opening angle (see ref [Ruiti condfluct PRB]) we estimate $\tilde{C}\approx ??C$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin conductance is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq ?? in Fredicikk]. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$. From these   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In a diffusive junction the Sharvin conductance is replaced by the Maxwell conductance, $G_\textrm{diffusive}=2a\sigma=\frac{8l}{3\pi a}G_\textrm{ballistic}$ [see eq ?? in Fredicikk]. On the other hand according to eq. ?? in [Fredicikk] the diffusive environment of the TLS yields a $K(\underline{\textbf{r}})_\textrm{diffusive}=\frac{l^2}{a^2}K(\underline{\textbf{r}})_\textrm{ballistic}$. From these   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C_\textrm{diffusive}}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\left(\frac{\Delta G}{G} \right)_\textrm{diffusive}=\tilde{C_\textrm{diffusive}}k_\textrm{F} \sqrt{\rho_\textrm{TLS}l^\frac{5}{2}\left(R_\textrm{M}G_0 \right)^\frac{3}{2}$$</div></td></tr>
</table>Halbritt