Anisotropy and Strong-Coupling Effects on the Collective Mode Spectrum of Chiral Superconductors: Application to Sr$_2$RuO$_4$

TL;DR

This paper develops a theoretical framework to analyze the collective bosonic excitations in anisotropic chiral superconductors like Sr$_2$RuO$_4$, revealing how anisotropy influences mode degeneracy, lifetimes, and experimental signatures.

Contribution

The authors introduce a time-dependent mean field theory for 2D chiral superconductors, elucidating the effects of anisotropy on bosonic mode spectra and decay channels.

Findings

Degeneracy of bosonic modes in 2D $^3$He-A is lifted by anisotropy.

Strong anisotropy causes low-lying fermionic states affecting bosonic mode decay.

Microwave excitation signatures can reveal anisotropic chiral superconductor properties.

Abstract

Recent theories of Sr$_2$RuO$_4$ based on the interplay of strong interactions, spin-orbit coupling and multi-band anisotropy predict chiral or helical ground states with strong anisotropy of the pairing states, with deep minima in the excitation gap, as well as strong phase anisotropy for the chiral ground state. We develop time-dependent mean field theory to calculate the Bosonic spectrum for the class of 2D chiral superconductors spanning $^3$He-A to chiral superconductors with strong anisotropy. Chiral superconductors support a pair of massive Bosonic excitations of the time-reversed pairs labeled by their parity under charge conjugation. These modes are degenerate for 2D $^3$He-A. Crystal field anisotropy lifts the degeneracy. Strong anisotropy also leads to low-lying Fermions, and thus to channels for the decay of the Bosonic modes. Selection rules and phase space considerations lead to large asymmetries in the lifetimes and hybridization of the Bosonic modes with the continuum of un-bound Fermion pairs. We also highlight results for the excitation of the Bosonic modes by microwave radiation that provide clear signatures of the Bosonic modes of an anisotropic chiral ground state.