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 $e^{i\mathbf{q}\cdot \mathbf{r}}$. Here, we theoretically investigate the stability of a stripe order, a weight-biased superposition state composed of $+\mathbf{q}$ and $-\mathbf{q}$ modes taking the form of ${\Delta }_{+}{e}^{i\mathbf{q}\cdot \mathbf{r}}+{\Delta }_{-}{e}^{-i\mathbf{q}\cdot \mathbf{r}}$ with $|{\Delta }_{+}|\ne |{\Delta }_{-}|\ne 0$, 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.

arXiv comment11 pages, 8 figures

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• Magnetoelectric effect in the helical state of a superconductor/ferromagnet bilayer
• Nonlinear diode effect and Berezinskii-Kosterlitz-Thouless transition in purely two-dimensional noncentrosymmetric superconductors
• Superconducting Diode Effect in Weak Localization Regime