Stripe order and diode effect in two-dimensional Rashba superconductors

Abstract

In two-dimensional superconductors with a Rashba-type spin-orbit coupling, it is known that an in-plane magnetic field can induce a helical superconducting (SC) state with a phase modulation $e^{i {\bf q}\cdot {\bf r}}$. Here, we theoretically investigate the stability of a stripe order, a weight-biased superposition state composed of $+{\bf q}$ and $-{\bf q}$ modes taking the form of $\Delta_+ e^{i{\bf q}\cdot{\bf r}}+\Delta_- e^{-i{\bf q}\cdot{\bf r}}$ with $|\Delta_+|\neq|\Delta_-|\neq 0$, assuming that the spin-singlet pairing channel is dominant. Based on the Ginzburg-Landau theory, we show that for both s-wave and d-wave pairing symmetries, the stripe order can appear in the high-field and low-temperature region inside the helical phase and that the transition between the helical and stripe phases is of second order. It is noteworthy that for the d-wave pairing, the stability region of the stripe phase shrinks when the in-plane field is rotated from the nodal direction to the anti-nodal direction. It is also found that the nonreciprocity of the critical current, the so-called SC diode effect, emerges not only in the helical phase but also in the stripe phase, with no clear nonreciprocity anomaly at the helical-stripe transition due to its second-order nature.