Admittance and critical current of nonreciprocal josephson junctions

The nonequilibrium current response in diffusive superconductor–normal-metal–superconductor junctions subjected to a low-frequency ac voltage is investigated. Using a kinetic description based on the adiabatic motion of Andreev bound states, we derive a general expression for the admittance of a junction under a dc phase bias, formulated entirely in terms of the phase-dependent density of states induced by the proximity effect. A numerical solution of the full nonlinear Usadel equations that describe the dynamics of the junction is presented. The obtained results for the admittance and the Josephson current-phase relation apply to two-dimensional planar junctions with Rashba spin-orbit coupling and an in-plane Zeeman field, as well as to Josephson junctions formed with topological insulator surface states as the normal layer. The frequency dependence of the admittance captures the crossover between the hydrodynamic and collisionless regimes, distinguished by the relation between the drive frequency and the inelastic relaxation rate in the normal region.