Alternating-current properties of short Josephson weak links

Abstract

We calculate the admittance of two types of Josephson weak links—the first is 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 superconducting reservoir and c is a constriction. The systems of the first type are analyzed on the basis of time-dependent Ginzburg-Landau equations derived by Gor'kov and Eliashberg for gapless superconductors with paramagnetic impurities. It is shown that the impedance Z(Ω) has a maximum as a function of the frequency Ω, and the electric field EΩ is determined by two gauge-invariant quantities. One of them is the condensate momentum QΩ and another is a 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 ETh=D/L2≫Δ), we present a formula for admittance Y valid frequencies Ω and temperatures T less than the Thouless energy ETh (ℏΩ,T≪ETh) but arbitrary with respect to the energy gap Δ. It is shown that, at low temperatures, the absorption is absent [Re(Y)=0] if the frequency does not exceed the energy gap in the center of the constriction (Ω<Δcosφ0, where 2φ0 is the phase difference between the S reservoirs). The absorption gradually increases with increasing the difference (Ω−Δcosφ0) if 2φ0 is less than the phase difference 2φc corresponding to the critical Josephson current. In the interval 2φc<2φ0<π, the absorption has a maximum. This interval of the phase difference is achievable in phase-biased Josephson junctions. Close to Tc the admittance has a maximum at low Ω, which is described by an analytical formula.

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