Optical and Raman selection rules for odd-parity clean superconductors

TL;DR

This paper derives optical and Raman selection rules to determine the parity of pairing order parameters in clean superconductors, aiding experimental identification of pairing symmetry in materials like doped Weyl semimetals and graphene.

Contribution

It introduces new selection rules linking optical spectra to pairing parity, applicable to chiral and singlet superconductors with specific symmetry conditions.

Findings

Selection rules distinguish pairing parity via optical gap measurements.

Application demonstrated in models of doped Weyl semimetals and graphene.

Discussion includes implications for twisted bilayer graphene.

Abstract

We derive selection rules in optical absorption and Raman scattering spectra, that can determine the parity of pairing order parameters under inversion symmetry in two classes of \emph{clean} superconductors: (i) chiral superconductors with strong spin-orbit couplings, (ii) singlet superconductors with negligible spin-orbit couplings. Experimentally, the inversion parity of pair wave functions can be determined by comparing the "optical gap" $\Delta_\text{op}$ in Raman and optical spectroscopy and the "thermodynamic gap" $2\Delta$ in specific heat measurements, and the selection rules apply when $\Delta_\text{op}>2\Delta$. We demonstrate the selection rules in superconductivity in models of (i) doped Weyl semimetals and (ii) doped graphene. Our derivation is based on the relation between pairing symmetry and fermion projective symmetry group of a superconductor. We further derive similar selection rules for two-dimensional superconductors with 2-fold rotational symmetry, and discuss how they apply to the superconducting state in magic-angle twisted bilayer graphene.