Transverse currents in triplet Josephson junction with spin-orbit coupling

Abstract

We investigate theoretically the equilibrium transverse charge and spin currents flowing in a hybrid Josephson junction composed of two triplet $p$-wave superconductors and a Rashba spin-orbit coupling (RSOC) layer in between. Through a symmetry analysis, we show that the transverse currents originate from the breaking of mirror symmetries due to the misalignment of $\mathbit{d}$ vectors in the two triplet superconductor leads. Besides, the mirror symmetries strongly constrain the dependence of the transverse currents on both the absolute and relative angles of the $\mathbit{d}$ vectors. The symmetry analysis is confirmed by the numerical calculations based on the lattice Matsubara Green's function method. The dependence of the transverse currents on the RSOC strength as well as the middle layer length is also addressed. These findings shed new light on the equilibrium spintronics device design and are useful for identifying the order parameter symmetries of $p$-wave superconductors.