Tuning current-phase relations with spin-orbit coupling in planar Josephson junctions

While current-phase relations (CPRs) in Josephson junctions (JJ) based on conventional s-wave superconductor are commonly considered to have a harmonic dependence, the breaking of spatial inversion symmetry and the tunability of the resulting spin-orbit coupling (SOC) provide a much more complex picture. At a fixed Zeeman field, a gate-controlled (SOC) in a JJ is responsible for the 0-pi ground-state phase difference or an anomalous intermediate phase, such that even at the zero-phase difference the supercurrent will flow in the junction [1,2].  The resulting CPRs can have strong anharmonicities and support spin-triplet superconductivity sought for both superconducting spintronics and Majorana bound states [2,3]. Here we examine various implications of the gate-controlled SOC on the evolution of CPRs and distinguish experimentally-relevant outcomes for the cases of the small and large chemical potential in JJs based on a two-dimensional electron gas.

 

[1] W. Mayer et al., Nat. Commun. 11, 212 (2020)

[2] M. Alidoust et al., PRB 103, L060503 (2021)

[3] M. C. Dartiailh et al., PRL 126, 036802 (2021)