# Signatures of Nematic Superconductivity in Doped Bi$_2$Se$_3$ under Applied Stress

## TL;DR

This paper investigates how applied stress affects nematic superconductivity in doped Bi$_2$Se$_3$, proposing experimental methods to verify the nematic nature of the order parameter and its impact on Josephson tunneling.

## Contribution

It develops a Ginzburg-Landau theoretical framework for nematic superconductors under stress and suggests experimental probes to confirm nematic order.

## Key findings

- Stress can be used to probe the nematic superconducting phase.
- Applied stress influences Josephson tunneling, acting as an on/off switch.
- Temperature dependence of critical current varies with stress, differing from conventional s-wave behavior.

## Abstract

The $M_x \text{Bi}_2 \text{Se}_3$ family are candidates for topological superconductors, where $M$ could be Cu, Sr, or Nb. Two-fold anisotropy has been observed in various experiments, prompting the interpretation that the superconducting state is nematic. However, it has since been recognized in the literature that a two-fold anisotropy in the upper critical field $H_{c2}$ is incompatible with the na\"{i}ve nematic hypothesis. In this paper we study the Ginzburg-Landau theory of a nematic order parameter coupled with an applied stress, and classify possible phase diagrams. Assuming that the $H_{c2}$ puzzle is explained by a pre-existing "pinning field", we indicate how a stress can be applied to probe an extended region of the phase diagram, and verify if the superconducting order parameter is indeed nematic. We also explore the Josephson tunneling between the proposed nematic superconducting state and an s-wave superconductor. The externally applied stress is predicted to serve as an on/off switch to the tunneling current, and in certain regime the temperature dependence of the critical current can be markedly different from that between two conventional s-wave superconductors.