Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems

TL;DR

This paper investigates phase transitions and symmetry breaking in frustrated three-band superconductors, revealing an unusual metallic state with broken time reversal symmetry and contrasting behaviors depending on the frustration strength.

Contribution

It introduces the concept of a metallic state with broken time reversal symmetry in three-band superconductors beyond mean field approximation.

Findings

Discovery of a metallic state with broken $ ext{Z}_2$ symmetry preceding superconductivity

Identification of fluctuation effects restoring symmetry at low frustration

Analysis of phase diagram with strong and weak frustration regimes

Abstract

We discuss the phase diagram and phase transitions in $U(1)\times \groupZ{2}$ three-band superconductors with broken time reversal symmetry. We find that beyond mean field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken $\groupZ{2}$ time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different $\groupZ{2}$ states is low and thus fluctuations restore broken time reversal symmetry in the superconducting state at low temperatures.