# Optical Properties of Bogoliubov Quasiparticles

## TL;DR

This paper calculates the optical conductivity of Bogoliubov quasiparticles, comparing with normal and superconducting states, and examines the effects of condensate response and phenomenological subtraction methods on optical scattering rates.

## Contribution

It provides a detailed calculation of the optical properties of BQP, including the condensate response, and evaluates the impact of a recent phenomenological subtraction procedure.

## Key findings

- Differences in optical scattering rates are largest just above the optical gap.
- The phenomenological subtraction causes deviations from BQP and superconducting state results.
- The superfluid density contributes a delta function at zero photon energy.

## Abstract

We calculated the optical conductivity $\sigma(T,\Omega)$ of a gas of Bogoliubov quasiparticles (BQP) from their Green's function and the Kubo formula. We compare with corresponding normal state (N) and superconducting state (SC) results. The superconducting case includes the dynamic response of the condensate through additional contributions to the Kubo formula involving the Gor'kov anomalous Green's function. The differences in the optical scattering rate are largest just above the optical gap and become progressively smaller as the photon energy is increased or the temperature is raised. Our results are compared with those obtained using a recently advocated phenomenological procedure for eliminating the effect of the condensate [1]. The $\delta$-function contribution at zero photon energy, proportional to the superfluid density, is dropped in the real part of the conductivity $[\sigma_1(T,\Omega)]$ and its Kramers-Kronig transform is subtracted from the imaginary part $\sigma_2(T,\Omega)$. This results in deviations from our BQP and superconducting state optical scattering rates even in the region where these have merged and are, in addition, close to the normal state result.