ac properties of short Josephson weak links

Abstract

The admittance of two types of Josephson weak links is calculated, i.e., of a one-dimensional superconducting wire with a local suppression of the order parameter, and the second is a short S-c-S structure, where S denotes a superconductor and c---a constriction. The systems of the first type are analyzed on the basis of time-dependent Ginzburg-Landau equations. We show that the impedance $Z(Ω)$ has a maximum as a function of the frequency $Ω$, and the electric field $E_Ω$ is determined by two gauge-invariant quantities---the condensate momentum $Q_Ω$ and the potential $μ$ related to charge imbalance. The structures of the second type are studied on the basis of microscopic equations for quasiclassical Green's functions in the Keldysh technique. For short S-c-S contacts (the Thouless energy ${E_{\text{Th}} = D/L^{2} \gg Δ}$) we present a formula for admittance $Y$ valid at frequencies $Ω$ and temperatures $T$ less than the Thouless energy but arbitrary with respect to the energy gap $Δ$. It is shown that, at low temperatures, the absorption is absent [${\mathrm{Re}(Y) = 0}$] if the frequency does not exceed the energy gap in the center of the constriction (${Ω< Δ\cos φ_{0}}$, where $2 φ_{0}$ is the phase difference between the S reservoirs). The absorption gradually increases with increasing the difference ${(Ω- Δ\cos φ_{0})}$ if $2 φ_{0}$ is less than the phase difference $2 φ_{\text{c}}$ corresponding to the critical Josephson current. In the interval ${2 φ_{\text{c}} < 2 φ_{0} < π}$, the absorption has a maximum. This interval of the phase difference is achievable in phase-biased Josephson junctions. Close to $T_{\text{c}}$ the admittance has a maximum at low $Ω$ which is described by an analytical formula.