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.

Graphical abstract

中文翻译：

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具有强自旋轨道耦合的导线中的非均匀超导性

摘要

我们在理论上研究存在Zeeman（或交换场）和自旋轨道耦合的一维单线非均匀超导的发生。使用格林函数形式主义，我们证明了自旋轨道耦合在宽范围的温度和塞曼场中稳定了调制的超导性。我们研究了温度-塞曼场相图的各向异性，该各向异性与塞曼场的方向有关。特别地，如果后一个场对准或垂直于导线方向，则不均匀的超导状态消失。我们确定了分别对应于弱和强自旋轨道耦合的两种状态。在两种情况下都评估了调制相位的波矢量。该结果也适用于由弱耦合的一维链制成的准一维超导体。

图形概要