Zero-temperature optical conductivity of ultraclean Fermi liquids and superconductors

A. Rosch; P. C. Howell

doi:10.1103/PhysRevB.72.104510

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Zero-temperature optical conductivity of ultraclean Fermi liquids and superconductors

A. Rosch, P. C. Howell

DOI 10.1103/PhysRevB.72.104510 · Physical Review B

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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 Γ∝ω2 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 (±π∕2,±π∕2), such that direct umklapp scattering among them is possible, one obtains Reσ(ω)∝ω2.