Time-Reversal Symmetry Breaking Superconductivity in CaSb${}_2$

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 $c\ast$-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.