# Time-reversal symmetry breaking superconductivity in hole-doped monolayer MoS$_{2}$

## TL;DR

This paper explores how hole doping in monolayer MoS₂ induces a unique time-reversal symmetry breaking superconducting state characterized by complex gap functions and finite angular momentum distributions, linked to Lifshitz transitions.

## Contribution

It introduces a realistic three-orbital model showing how Lifshitz transitions lead to time-reversal breaking superconductivity in noncentrosymmetric, spin-orbit-coupled monolayer materials.

## Key findings

- Lifshitz transition causes a sign change in the pairing phase.
- Time-reversal breaking phase exhibits complex gap functions.
- Finite momentum-space distributions of orbital and spin angular momentum are observed.

## Abstract

We investigate the nature of the time-reversal breaking pairing state in the hole-doped monolayer MoS$_{2}$ on the basis of the realistic three-orbital attractive Hubbard-like model with the atomic spin-orbit coupling. Due to the multi-band features arising from the Mo $d$ orbitals in the noncentrosymmetric crystal structure, the Lifshitz transition takes place upon hole doping. Across the Lifshitz transition point, the sign of the relative phase between the Cooper-pair components drastically changes, leading to the emergence of the time-reversal breaking phase with complex gap functions. It is shown that this intriguing pairing state is characterized by the finite momentum-space distributions of the orbital and spin angular momentum with three-fold rotational symmetry on the Fermi-surface pockets around K and K$'$ points. The present mechanism for the time-reversal breaking superconductivity can ubiquitously be applied to spin-orbit-coupled metals in noncentrosymmetric crystal structures.