Adiabatic Dynamics of Superconducting Quantum Point Contacts

TL;DR

This paper derives a universal kinetic equation for the ac Josephson effect in superconducting quantum point contacts, enabling analysis of their dynamic conductance and current-voltage characteristics under arbitrary time-dependent voltages.

Contribution

It introduces a simple, broadly applicable kinetic equation for superconducting quantum point contacts that unifies previous approaches and confirms the microscopic current expression.

Findings

Frequency-dependent linear conductance calculated.

Dc I-V characteristics with microwave radiation analyzed.

Excess current of 2I_c/π observed at small voltages.

Abstract

Starting from the quasiclassical equations for non-equilibrium Green's functions we derive a simple kinetic equation that governs ac Josephson effect in a superconducting quantum point contact at small bias voltages. In contrast to existing approaches the kinetic equation is valid for voltages with arbitrary time dependence. We use this equation to calculate frequency-dependent linear conductance, and dc $I\!-\!V$ characteristics with and without microwave radiation for resistively shunted quantum point contacts. A novel feature of the $I\!-\!V$ characteristics is the excess current $2I_c/\pi$ appearing at small voltages. An important by-product of our derivation is the analytical proof that the microscopic expression for the current coincides at arbitrary voltages with the expression that follows from the Bogolyubov-de Gennes equations, if one uses appropriate amplitudes of Andreev reflection which contain information about microscopic structure of the superconductors.