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 $Z(\Omega )$ has a maximum as a function of the frequency $\Omega$, and the electric field $E_{\Omega }$ is determined by two gauge-invariant quantities---the condensate momentum $Q_{\Omega }$ and the potential $\mu$ 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 $E_{\text{Th}}=D/L^2\gg \Delta$) we present a formula for admittance $Y$ valid at frequencies $\Omega$ and temperatures $T$ less than the Thouless energy but arbitrary with respect to the energy gap $\Delta$. 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 ($\Omega <\Delta \cos {\phi }_0$, where $2{\phi }_0$ is the phase difference between the S reservoirs). The absorption gradually increases with increasing the difference $(\Omega -\Delta \cos {\phi }_0)$ if $2{\phi }_0$ is less than the phase difference $2{\phi }_{\text{c}}$ corresponding to the critical Josephson current. In the interval $2{\phi }_{\text{c}}<2{\phi }_0<\pi$, 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 $\Omega$ which is described by an analytical formula.

published version

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Cited by in corpus (1)

• Static and dynamic properties of Josephson weak links with singlet and triplet coupling