Zero-temperature optical conductivity of ultraclean Fermi liquids and superconductors

A. Rosch and P. C. Howell
Phys. Rev. B 72, 104510 – Published 13 September 2005

Abstract

We calculate the low-frequency optical conductivity σ(ω) of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of σ have very little in common. For small Fermi surfaces in three dimensions (but not in two dimensions) we find, for example, that Reσ(ω>0)const which corresponds to a scattering rate Γω2 even in the absence of umklapp scattering when there is no T2 contribution to Γ. In the main part of the paper we discuss in detail the optical conductivity of d-wave superconductors in two dimensions where Reσ(ω>0)ω4 for the smallest frequencies and the umklapp processes typically set in smoothly above a finite threshold ω0 smaller than twice the maximal gap Δ. In cases where the nodes are located at (±π2,±π2), such that direct umklapp scattering among them is possible, one obtains Reσ(ω)ω2.

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  • Received 1 April 2005

DOI:https://doi.org/10.1103/PhysRevB.72.104510

©2005 American Physical Society

Authors & Affiliations

A. Rosch

  • Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany

P. C. Howell

  • Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, D-76128 Karlsruhe, Germany

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Vol. 72, Iss. 10 — 1 September 2005

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