Probing spin--orbit coupling and in-plane Zeeman effects in SNS junctions of two-dimensional hole gases

We investigate theoretically a Josepshon junction consisting of a 2D hole gas with Rashba spin-orbit coupling and a Zeeman effect coupled to two superconducting leads. We develop a semi-classical theory to describe the critical current of the junction in response to an applied in-plane magnetic field and we investigate the resulting dependence of the supercurrent, both numerically and analytically. We find qualitatively different patterns of critical current in different physically relevant regimes and we connect the observed features to the underlying model parameters. Our theory could thus be used for characterization of 2D hole gases, potentially even revealing quantitative information about parameters such as the effective strength of the spin-orbit interaction and the in-plane g-factor.