Stripe order and diode effect in two-dimensional Rashba superconductors
Kazushi Aoyama
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 ${e}^{i\mathbf{q}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{r}}$. Here, we theoretically investigate the stability of a stripe order, a weight-biased superposition state composed of $+\mathbf{q}$ and $\ensuremath{-}\mathbf{q}$ modes taking the form of ${\mathrm{\ensuremath{\Delta}}}_{+}{e}^{i\mathbf{q}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{r}}+{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}{e}^{\ensuremath{-}i\mathbf{q}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{r}}$ with $|{\mathrm{\ensuremath{\Delta}}}_{+}|\ensuremath{\ne}|{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}|\ensuremath{\ne}0$, assuming that the spin-singlet pairing channel is dominant. Based on the Ginzburg-Landau theory, we show that for both $s$- 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 antinodal 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.