Admittance of a long diffusive SNS junction

The dynamical properties of hybrid normal metal/superconductor structures have recently come into research focus both experimentally and theoretically. Recent experimental studies of the coherent admittance $Y\left(\omega \right)$ of SNS rings as a function of the phase difference ${\varphi }_0$ are still not fully understood. Here we concentrate on the linear response regime, calculating $Y\left(\omega \right)$ by solving the Usadel equations, linearized in an electric field. Partially reproducing previously known results, we find qualitatively different behavior in the collisionless regime of ${\tau }_{\text{in}}^{-1}\ll \omega \lesssim E_{\text{Th}}$ and high temperature $T\gg E_{\text{Th}}$ and low temperature $T\lesssim E_{\text{Th}}$ near the minigap closing ${\varphi }_0\sim \pi$. We find that the dissipative part $\text{Re}Y\left(\omega \right)$ peaks when the minigap closes (at a phase difference of $\pi$) even at high temperatures, when the equilibrium supercurrent is fully suppressed.

Figure 1

Left: Function $Q\left({\varphi }_0\right)$ entering Lempitskii's prediction for the coherent part of the dissipation. Right: Dissipative response at $T\approx 17E_{\text{Th}}$, data from Ref. [13]. Blue curve: Hydrodynamic regime, $\hslash \omega =0.4E_{\text{Th}}$, red curve: collisionless regime, $\hslash \omega =2E_{\text{Th}}$ (arbitrary shifted in the $c$ axis).

Figure 2

Variation of the longitudinal distribution function at $T=15E_{\text{Th}}$, $\hslash \omega =E_{\text{Th}}$ with varying the phase difference $g=40$.

Figure 3

Variation of the transversal distribution function at $T=15E_{\text{Th}}$, $\hslash \omega =E_{\text{Th}}$ with varying the phase difference $g=40$.

Figure 4

Variation of $\text{Re}Y\left({\varphi }_0\right)/Y_N$ with frequency at $T=15E_{\text{Th}}$, $g=40$, low frequencies.

Figure 5

Variation of $\text{Re}Y\left({\varphi }_0\right)/Y_N$ with frequency at $T=15E_{\text{Th}}$, $g=40$, high frequencies.

Figure 6

Variation of $\text{Re}Y\left({\varphi }_0\right)/Y_N$ with temperature at $\hslash \omega =E_{\text{Th}}$, $g=40$.

Figure 7

Variation of $\text{Re}Y\left({\varphi }_0\right)/Y_N$ with frequency at $T=E_{\text{Th}}$, $g=40$.

Figure 8

Variation of $\text{Re}Y\left({\varphi }_0\right)/Y_N$ with temperature at $\omega =0.3E_{\text{Th}}$, $g=20$.

Figure 9

Variation of $\text{Im}Y\left({\varphi }_0\right)/Y_N$ with temperature at $\omega =5E_{\text{Th}}$, $g=20$.