# Optical properties of Bogoliubov quasiparticles

Ewald Schachinger, Jules P. Carbotte

Research output: Contribution to journalArticleResearchpeer-review

### 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.\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.
Original language English 144516 9 Physical Review / B 95 https://doi.org/10.1103/PhysRevB.95.144516 Published - 2017

### Fingerprint

Green's function
condensates
Green's functions
Optical properties
Scattering
Optical conductivity
Delta functions
optical properties
conductivity
delta function
dynamic response
scattering
Dynamic response
Photons
Gases
deviation
photons
gases
Temperature
temperature

### Keywords

• Superconductivity

### ASJC Scopus subject areas

• Condensed Matter Physics

• Sonstiges

### Treatment code (Nähere Zuordnung)

• Basic - Fundamental (Grundlagenforschung)

### Cite this

Optical properties of Bogoliubov quasiparticles. / Schachinger, Ewald; Carbotte, Jules P.

In: Physical Review / B, Vol. 95, 2017, p. 144516.

Research output: Contribution to journalArticleResearchpeer-review

Schachinger, Ewald ; Carbotte, Jules P. / Optical properties of Bogoliubov quasiparticles. In: Physical Review / B. 2017 ; Vol. 95. pp. 144516.
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N2 - We calculated the optical conductivity $\sigma(T,\Omega)$ of a gas ofBogoliubov quasiparticles (BQP) from their Green's function and theKubo formula. We compare with corresponding normal state (N) andsuperconducting state (SC) results. The superconducting case includesthe dynamic response of the condensate through additional contributionsto the Kubo formula involving the Gor'kov anomalous Green's function.The differences in the optical scattering rate are largest justabove the optical gap and become progressively smaller as the photonenergy is increased or the temperature is raised. Our results arecompared with those obtained using a recently advocated phenomenologicalprocedure for eliminating the effect of the condensate.\cite{dord2014}The $\delta$-function contribution at zero photon energy, proportional tothe superfluid density, is dropped in the real part of the conductivity$[\sigma_1(T,\Omega)]$ and its Kramers-Kronig transform is subtracted fromthe imaginary part $\sigma_2(T,\Omega)$. This results in deviations fromour BQP and superconducting state optical scattering rates even in theregion where these have merged and are, in addition, close to the normalstate result.

AB - We calculated the optical conductivity $\sigma(T,\Omega)$ of a gas ofBogoliubov quasiparticles (BQP) from their Green's function and theKubo formula. We compare with corresponding normal state (N) andsuperconducting state (SC) results. The superconducting case includesthe dynamic response of the condensate through additional contributionsto the Kubo formula involving the Gor'kov anomalous Green's function.The differences in the optical scattering rate are largest justabove the optical gap and become progressively smaller as the photonenergy is increased or the temperature is raised. Our results arecompared with those obtained using a recently advocated phenomenologicalprocedure for eliminating the effect of the condensate.\cite{dord2014}The $\delta$-function contribution at zero photon energy, proportional tothe superfluid density, is dropped in the real part of the conductivity$[\sigma_1(T,\Omega)]$ and its Kramers-Kronig transform is subtracted fromthe imaginary part $\sigma_2(T,\Omega)$. This results in deviations fromour BQP and superconducting state optical scattering rates even in theregion where these have merged and are, in addition, close to the normalstate result.

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