Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1704.02727 · Physical review. B./Physical review. B

Optical properties of Bogoliubov quasiparticles

E. Schachinger, J. P. Ćarbotte

Published Apr 27, 2017• 2 citations
arXivHTMLPDF

Abstract

We calculate the optical conductivity $\ensuremath{\sigma}(T,\mathrm{\ensuremath{\Omega}})$ of a gas of Bogoliubov quasiparticles from their Green's function and the Kubo formula. We make comparisons with corresponding normal-state and superconducting-state 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. In this procedure the $\ensuremath{\delta}$-function contribution at zero photon energy, proportional to the superfluid density, is dropped in the real part of the conductivity $[{\ensuremath{\sigma}}_{1}(T,\mathrm{\ensuremath{\Omega}})]$ and its Kramers-Kronig transform is subtracted from the imaginary part ${\ensuremath{\sigma}}_{2}(T,\mathrm{\ensuremath{\Omega}})$. This results in deviations from our Bogoliubov quasiparticle and superconducting-state optical scattering rates even in the region where these have merged and are, in addition, not close to the normal-state result.

DOI
10.1103/physrevb.95.144516

Related papers

Optical response of correlated electron systems

Dmitrii L Maslov, Andrey V Chubukov

Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, [Formula: see text]. This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) [Formula: see text] scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermi-liquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, [Formula: see text], and show that a factor of [Formula: see text] is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that [Formula: see text] must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient b in the Gurzhi-like form, [Formula: see text], differs significantly from b = 4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b = 1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on 'composite' scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T = 0: [Formula: see text] at low frequencies and [Formula: see text] at higher frequencies. We also discuss [Formula: see text] scaling of the conductivity and show that [Formula: see text] in the same model scales in a non-Fermi-liquid way, as [Formula: see text].

arXiv:1608.02514•Reports on Progress in Physics•Dec 21, 2016•97 citations

Temperature-dependent low-frequency conductivity in marginal-Fermi-liquid theory

E. J. Nicol, J. P. Ćarbotte

We have calculated the temperature-dependent optical conductivity within phenomenological marginal-Fermi-liquid theory. A ``coherencelike'' peak occurs from a drop in the quasiparticle damping in the superconducting state. Results are given for varying impurity scattering rate.

Physical review. B, Condensed matter•Oct 1, 1991•52 citations

Pseudogap in the c -axis (along the ladder) optical conductivity of t − J ladders and its quasiparticle interpretation

Paulína Karlubíková, Hana Růžičková, Jiří Chaloupka +1 more

Motivated by similarities between cuprate superconductors and two-leg ladder copper-oxide compounds and in order to obtain a better understanding of optical properties of cuprate superconductors we have studied the c-axis (along the ladder) optical conductivity [Formula: see text] of a doped [Formula: see text] two-leg ladder. Using exact diagonalization, we have calculated the conductivity and related quantities for cyclic ladders of up to 13 rungs. In agreement with results of an early study by Hayward and coworkers (Hayward et al 1996 Phys. Rev. B 53 8863) we find that [Formula: see text] consists of a Drude peak at zero frequency and an absorption band in the infrared region that is separated from the former by a pseudogap. The width of the pseudogap [Formula: see text] increases with increasing J/t, in parallel with an increase of the magnitude [Formula: see text] of the gap in the quasiparticle excitation spectra. Our central finding is that [Formula: see text], where [Formula: see text] is the magnitude of the gap in the spin excitation spectra. We demonstrate that this approximate relation can be understood in terms of a phenomenological model involving a superconducting ladder and a coupling between charged quasiparticles and spin excitations. The relation is remarkably similar to the one between experimental values of the energy scale of a dip in the in-plane optical conductivity, the superconducting gap [Formula: see text] and the energy of the spin-resonance in cuprate superconductors (for a recent discussion of the optical data, see Šopík et al 2015 New J. Phys. 17 053022). Our findings support the point of view that low energy infrared active excited states of cuprate superconductors can be viewed as consisting of two charged quasiparticles connected with pair-breaking and a spin excitation.

Journal of Physics Condensed Matter•Jan 9, 2019•1 citation

Zero-temperature optical conductivity of ultraclean Fermi liquids and superconductors

Achim Rosch, P. C. Howell

We calculate the low-frequency optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of $\ensuremath{\sigma}$ have very little in common. For small Fermi surfaces in three dimensions (but not in two dimensions) we find, for example, that $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\sigma}(\ensuremath{\omega}>0)\ensuremath{\approx}\mathrm{const}$ which corresponds to a scattering rate $\ensuremath{\Gamma}\ensuremath{\propto}{\ensuremath{\omega}}^{2}$ even in the absence of umklapp scattering when there is no ${T}^{2}$ contribution to $\ensuremath{\Gamma}$. In the main part of the paper we discuss in detail the optical conductivity of $d$-wave superconductors in two dimensions where $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\sigma}(\ensuremath{\omega}>0)\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ for the smallest frequencies and the umklapp processes typically set in smoothly above a finite threshold ${\ensuremath{\omega}}_{0}$ smaller than twice the maximal gap $\ensuremath{\Delta}$. In cases where the nodes are located at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}∕2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}∕2)$, such that direct umklapp scattering among them is possible, one obtains $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{2}$.

arXiv:cond-mat/0503718•Physical Review B•Sep 13, 2005•34 citations

Optical conductivity and kinetic energy of the superconducting state: A cluster dynamical mean field study

Kristjan Haule, Gabriel Kotliar

We study the evolution of the optical conductivity in the t-J model with temperature and doping using the Extended Dynamical Cluster Approximation. The cluster approach results in an optical mass which is doping independent near half filling. The transition to the superconducting state in the overdoped regime is characterized by a decrease in the hole kinetic energy, in contrast to the underdoped side where kinetic energy of holes increases upon superfluid condensation. In both regimes, the optical conductivity displays anomalous transfers of spectral weight over a broad frequency region.

arXiv:cond-mat/0601478•Europhysics Letters (EPL)•Jan 1, 2007•52 citations

Thermal conductivity of an ultracold Fermi gas in the BCS-BEC crossover

Hang Zhou, Yong-li Ma

Recent experiments on sound waves in a unitary Fermi gas reveal many transport properties about strongly interacting fermions. Sound propagates through the coupling of momentum and heat transport, and attenuates strongly with the presence of a phase transition. In this work, focusing on the temperature regimes near and below the superfluid critical temperature [Formula: see text] in the BCS-BEC crossover, we present a Kubo-based microscopic calculation of thermal conductivity [Formula: see text], which has not attracted much attention compared to the shear viscosity. Our approach primarily addresses the contributions of the fermionic quasiparticles to thermal transport and our results return to the kinetic descriptions at high temperatures. [Formula: see text] drops upon crossing the pseudogap temperature [Formula: see text], and its temperature dependence changes below [Formula: see text]. The drops become more pronounced on the weakly coupled BCS side, where the Pauli blocking causes the upturn of [Formula: see text] above [Formula: see text]. Our calculations fit well with the sound measurement on the damping rate.

Scientific Reports•Jan 13, 2021•8 citations
We calculate the optical conductivity \ensuremathσ(T,\ensuremathΩ)\ensuremath{\sigma}(T,\mathrm{\ensuremath{\Omega}})\ensuremathσ(T,\ensuremathΩ) of a gas of Bogoliubov quasiparticles from their Green's function and the Kubo formula. We make comparisons with corresponding normal-state and superconducting-state 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. In this procedure the \ensuremathδ\ensuremath{\delta}\ensuremathδ-function contribution at zero photon energy, proportional to the superfluid density, is dropped in the real part of the conductivity [\ensuremathσ1(T,\ensuremathΩ)][{\ensuremath{\sigma}}_{1}(T,\mathrm{\ensuremath{\Omega}})][\ensuremathσ1​(T,\ensuremathΩ)] and its Kramers-Kronig transform is subtracted from the imaginary part \ensuremathσ2(T,\ensuremathΩ){\ensuremath{\sigma}}_{2}(T,\mathrm{\ensuremath{\Omega}})\ensuremathσ2​(T,\ensuremathΩ). This results in deviations from our Bogoliubov quasiparticle and superconducting-state optical scattering rates even in the region where these have merged and are, in addition, not close to the normal-state result.
Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, [Formula: see text]. This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) [Formula: see text] scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermi-liquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, [Formula: see text], and show that a factor of [Formula: see text] is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that [Formula: see text] must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient b in the Gurzhi-like form, [Formula: see text], differs significantly from b = 4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b = 1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on 'composite' scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T = 0: [Formula: see text] at low frequencies and [Formula: see text] at higher frequencies. We also discuss [Formula: see text] scaling of the conductivity and show that [Formula: see text] in the same model scales in a non-Fermi-liquid way, as [Formula: see text].
Motivated by similarities between cuprate superconductors and two-leg ladder copper-oxide compounds and in order to obtain a better understanding of optical properties of cuprate superconductors we have studied the c-axis (along the ladder) optical conductivity [Formula: see text] of a doped [Formula: see text] two-leg ladder. Using exact diagonalization, we have calculated the conductivity and related quantities for cyclic ladders of up to 13 rungs. In agreement with results of an early study by Hayward and coworkers (Hayward et al 1996 Phys. Rev. B 53 8863) we find that [Formula: see text] consists of a Drude peak at zero frequency and an absorption band in the infrared region that is separated from the former by a pseudogap. The width of the pseudogap [Formula: see text] increases with increasing J/t, in parallel with an increase of the magnitude [Formula: see text] of the gap in the quasiparticle excitation spectra. Our central finding is that [Formula: see text], where [Formula: see text] is the magnitude of the gap in the spin excitation spectra. We demonstrate that this approximate relation can be understood in terms of a phenomenological model involving a superconducting ladder and a coupling between charged quasiparticles and spin excitations. The relation is remarkably similar to the one between experimental values of the energy scale of a dip in the in-plane optical conductivity, the superconducting gap [Formula: see text] and the energy of the spin-resonance in cuprate superconductors (for a recent discussion of the optical data, see Šopík et al 2015 New J. Phys. 17 053022). Our findings support the point of view that low energy infrared active excited states of cuprate superconductors can be viewed as consisting of two charged quasiparticles connected with pair-breaking and a spin excitation.
We calculate the low-frequency optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of $\ensuremath{\sigma}$ have very little in common. For small Fermi surfaces in three dimensions (but not in two dimensions) we find, for example, that $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\sigma}(\ensuremath{\omega}>0)\ensuremath{\approx}\mathrm{const}$ which corresponds to a scattering rate $\ensuremath{\Gamma}\ensuremath{\propto}{\ensuremath{\omega}}^{2}$ even in the absence of umklapp scattering when there is no T2{T}^{2}T2 contribution to $\ensuremath{\Gamma}$. In the main part of the paper we discuss in detail the optical conductivity of ddd-wave superconductors in two dimensions where $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\sigma}(\ensuremath{\omega}>0)\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ for the smallest frequencies and the umklapp processes typically set in smoothly above a finite threshold ${\ensuremath{\omega}}_{0}$ smaller than twice the maximal gap $\ensuremath{\Delta}$. In cases where the nodes are located at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}∕2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}∕2)$, such that direct umklapp scattering among them is possible, one obtains $\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{2}$.
We study the evolution of the optical conductivity in the t-J model with temperature and doping using the Extended Dynamical Cluster Approximation. The cluster approach results in an optical mass which is doping independent near half filling. The transition to the superconducting state in the overdoped regime is characterized by a decrease in the hole kinetic energy, in contrast to the underdoped side where kinetic energy of holes increases upon superfluid condensation. In both regimes, the optical conductivity displays anomalous transfers of spectral weight over a broad frequency region.
Recent experiments on sound waves in a unitary Fermi gas reveal many transport properties about strongly interacting fermions. Sound propagates through the coupling of momentum and heat transport, and attenuates strongly with the presence of a phase transition. In this work, focusing on the temperature regimes near and below the superfluid critical temperature [Formula: see text] in the BCS-BEC crossover, we present a Kubo-based microscopic calculation of thermal conductivity [Formula: see text], which has not attracted much attention compared to the shear viscosity. Our approach primarily addresses the contributions of the fermionic quasiparticles to thermal transport and our results return to the kinetic descriptions at high temperatures. [Formula: see text] drops upon crossing the pseudogap temperature [Formula: see text], and its temperature dependence changes below [Formula: see text]. The drops become more pronounced on the weakly coupled BCS side, where the Pauli blocking causes the upturn of [Formula: see text] above [Formula: see text]. Our calculations fit well with the sound measurement on the damping rate.