Theory of optical responses in clean multi-band superconductors

TL;DR

This paper develops a theoretical framework explaining how intrinsic momentum-conserving optical excitations occur in clean multi-band superconductors under certain symmetry conditions, challenging traditional dirty-limit assumptions.

Contribution

It introduces a symmetry-based theory for optical responses in clean multi-band superconductors, highlighting conditions for intrinsic excitations beyond inversion symmetry breaking.

Findings

Intrinsic optical excitations occur under specific symmetry conditions.

Application to FeSe demonstrates the theory's relevance.

Challenges the conventional dirty-limit understanding of optical responses.

Abstract

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.