Admittance and critical current of nonreciprocal Josephson junctions

TL;DR

This work develops a kinetic, adiabatic description of the nonequilibrium AC response in diffusive SNS junctions, deriving a general low-frequency admittance formula that depends solely on the phase-dependent density of states $\nu(\epsilon,\phi)$. The approach bridges the proximity-induced minigap physics with spectral-flow-driven quasiparticle dynamics, yielding ${\rm Re}\,\Upsilon(\omega,\phi_0) = \Upsilon_N (E_T/T) (\tau_{in} E_T)/(1+(\omega \tau_{in})^2) \, Q(\phi_0,T)$ and a contribution from the AC supercurrent, with $Q(\phi_0,T)$ defined by DOS-weighted integrals. Using Usadel theory, the authors analyze a diffusive planar SNS junction with Rashba SOC and an in-plane Zeeman field, showing that a field-induced phase shift $\delta\phi = 2\tau_{so}\alpha_R h L / D$ shifts the DOS and thus $Q$, implying nonreciprocal dissipative responses when inversion and time-reversal symmetries are broken; however, in the diffusive limit this nonreciprocity is strongly suppressed. The results extend to superconductor–topological-insulator–superconductor junctions and offer a framework to extract DOS information from admittance measurements, with potential relevance for superconducting diode effects and multiterminal junction designs.

Abstract

We investigate the nonequilibrium current response in diffusive superconductor-normal-metal-superconductor junctions subjected to a low-frequency AC voltage. 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.

Figures (6)

• Figure 1: Top down view of a planar SNS junction. The junction is aligned along the $\hat{\bf x}$ direction, there is a parallel magnetic field ${\bf H}$ directed in the $\hat{\bf y}$ direction, and there is an out of plane vector $\hat{\bf n}$ pointing in the $\hat{\bf z}$ direction from the spin-orbit effect that breaks inversion symmetry.
• Figure 2: Numerically calculated density of states in a diffusive SNS junction from the solution of Usadel equations \ref{['eq:Usadel']} plotted for various phase differences $\phi_0$. The energy is normalized by the Thouless energy $E_T$.
• Figure 3: The top panel shows numerically calculated density of states in a diffusive SNS junction plotted for a sufficiently high magnetic field $h=5E_T$ at two representative values of the phase $\phi_0$ across the junction. The values of other control parameters related to the strength of spin-orbit are listed on the plot. The bottom panel shows sensitivity of the energy levels $V_\nu(\epsilon,\phi_0)$ to a change in the phase difference plotted for the same set of parameters.
• Figure 4: Variation of the dimensionless admittance function of a long SNS junction as a function of temperature and magnetic field. Parameters of the plot are shown for each line.
• Figure 5: Josephson current-phase relation of a long SNS junction computed as a function of temperature and in-plane magnetic field for the Rashba-Zeeman model.