# Non uniform superconductivity in wires with strong spin-orbit coupling

## TL;DR

This paper theoretically investigates how strong spin-orbit coupling influences the emergence and stability of nonuniform superconductivity in one-dimensional wires under Zeeman fields, revealing anisotropic phase diagrams and regimes of modulated states.

## Contribution

It introduces a comprehensive Green's function analysis of nonuniform superconductivity in 1D wires with spin-orbit coupling, identifying conditions for stability and wave-vector characteristics.

## Key findings

- Spin-orbit coupling stabilizes modulated superconductivity over a broad temperature and field range.
- The phase diagram's anisotropy depends on the Zeeman field orientation relative to the wire.
- Two regimes of weak and strong spin-orbit coupling exhibit distinct wave-vectors for the modulated phase.

## Abstract

We study theoretically the onset of nonuniform superconductivity in a one-dimensional single wire in presence of Zeeman (or exchange field) and spin-orbit coupling. Using the Green's function formalism, we show that the spin-orbit coupling stabilizes modulated superconductivity in a broad range of temperatures and Zeeman fields. We investigate the anisotropy of the temperature-Zeeman field phase diagram, which is related to the orientation of the Zeeman field. In particular, the inhomogeneous superconducting state disappears if this latter field is aligned or perpendicular to the wire direction. We identify two regimes corresponding to weak and strong spin-orbit coupling respectively. The wave-vector of the modulated phase is evaluated in both regimes. The results also pertain for quasi-1D superconductors made of weakly coupled 1D chains.