Model of collective modes in three-band superconductors with repulsive interband interactions

TL;DR

This paper models three-band superconductors with repulsive interactions, revealing complex collective modes arising from frustration and time-reversal symmetry breaking, which couple phase and amplitude oscillations.

Contribution

It introduces a simple microscopic model to analyze collective modes in three-band superconductors with repulsive interband interactions, highlighting novel mixed phase-amplitude oscillations.

Findings

Identification of two distinct collective modes with energies below twice the gap.

Presence of these modes for all interband coupling values.

Demonstration of complex order parameters breaking time-reversal symmetry.

Abstract

I consider a simple model of a three-band superconductor with repulsive interband interactions. The frustration, associated with the odd number of bands, leads to the possible existence of an intrinsically complex time-reversal symmetry breaking (TRSB) order parameter. In such state the fluctuations of the different gaps are strongly coupled, and this leads to the development of novel collective modes, which mix phase and amplitude oscillations. I study these fluctuations using a simple microscopic model and derive the dispersion for two physically distinct modes, which are gapped by energy less than twice the gap, and apparently present for all values of interband couplings.