Josephson diode effect via a non-equilibrium Rashba system

Abstract

A non-equilibrium state in a Rashba system under an in-plane magnetic field is identified as the origin of the Josephson diode effect. This state is induced by a current bias--necessary for measuring the current-voltage characteristics--which shifts the Fermi momentum away from equilibrium. This essential mechanism has been overlooked in previous studies. This oversight stems from the implicit assumption that the equilibrium-based formulations are sufficient to describe Josephson effect. We formulate the Josephson coupling via the non-equilibrium Rashba system under current bias using a tunneling Hamiltonian, where the Rashba system is modeled as one-dimensional. When the magnetic field is applied perpendicular to the current, the Josephson coupling becomes asymmetric, giving rise to the diode effect. The magnitude and sign of this effect depend on the distance between the superconducting electrodes $d$, the in-plane magnetic field, and the spin-orbit coupling strength. Our results clarify the microscopic origin of the Josephson diode effect, which can be optimized by tuning $d$.