Optical properties of Bogoliubov quasiparticles

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.\cite{dord2014}
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.