# Topological Superconductivity Intertwined with Broken Symmetries

## TL;DR

This paper investigates the nature of topological superconducting states on the surface of PbTaSe$_2$, revealing conditions under which time-reversal symmetry is broken and identifying two distinct topological states.

## Contribution

It introduces a microscopic two-channel model and identifies conditions leading to time-reversal symmetry breaking in topological superconductors with broken inversion symmetry.

## Key findings

- Two types of topological superconducting states identified
- Time-reversal symmetry breaking is unavoidable under certain conditions
- Guides future search for topological chiral superconductors

## Abstract

Recently the superconductor and topological semimetal PbTaSe$_2$ was experimentally found to exhibit surface-only lattice rotational symmetry breaking below $T_c$. We exploit the Ginzburg-Landau free energy and propose a microscopic two-channel model to study possible superconducting states on the surface of PbTaSe$_2$. We identify two types of topological superconducting states. One is time-reversal invariant and preserves the lattice hexagonal symmetry while the other breaks both symmetries. We find that such time-reversal symmetry breaking is unavoidable for a superconducting state in a two dimensional irreducible representation of crystal point group in a system where the spatial inversion symmetry is broken and the strong spin-orbit coupling is present. Our findings will guide the search for topological chiral superconductors.