Time-Reversal Symmetry Breaking Superconductivity in CaSb$_2$

TL;DR

This study reveals that CaSb$_2$ exhibits time-reversal symmetry breaking superconductivity with an $s+is$ order parameter, involving complex interband interactions and potential loop currents, making it a promising platform for topological superconductivity.

Contribution

It provides the first evidence of TRS-breaking superconductivity in CaSb$_2$ and proposes a novel $s+is$ order parameter with direction-dependent TRS breaking.

Findings

TRS breaking indicated by muon spin relaxation data.

Superconductivity described by single-gap or two-gap models.

Proposed loop currents in Sb plane as TRS breaking mechanism.

Abstract

CaSb$_2$ is a bulk superconductor and a topological semimetal, making it a great platform for realizing topological superconductivity. In this work, we investigate the superconducting upper and lower critical field anisotropy using magnetic susceptibility, and study the superconducting state using muon spin-relaxation. The temperature dependence of transverse-field relaxation rate can be fitted with a single-gap model or two-gap model. Zero-field relaxation shows little temperature dependence when the muon-spin is parallel to the $c*$-axis, while an increase in relaxation appears below 1 K when the muon-spin is parallel to the $ab$-plane. We conclude an $s+is$ order parameter considering the breaking of time-reversal symmetry (TRS), which originates from competing interband interactions between the three bands of CaSb$_2$. To explain the direction-dependent breaking of TRS we suggest loop currents developing in the plane of distorted square-net of Sb atoms.