Fermi surface geometry and optical conductivity of a two-dimensional electron gas near an Ising-nematic quantum critical point

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Abstract

We analyze optical conductivity of a clean two-dimensional electron system in a Fermi liquid regime near a T=0 Ising-nematic quantum critical point (QCP) and extrapolate the results to a QCP. We employ direct perturbation theory up to the two-loop order to elucidate how the Fermi surface's geometry (convex vs concave) and fermionic dispersion (parabolic vs nonparabolic) affect the scaling of the optical conductivity σ(ω) with frequency ω and correlation length ζ. We find that for a convex Fermi surface the leading terms in the optical conductivity cancel out, leaving a subleading contribution σ(ω)∝ω2ζ4L, where L=const for a parabolic dispersion and L∝lnωζ3 in a generic case. For a concave Fermi surface, the leading terms do not cancel, and σ(ω)∝ζ2. We extrapolate these results to a QCP and obtain σ(ω)∝ω2/3 for a convex Fermi surface and σ(ω)∝1/ω2/3 for a concave Fermi surface.

Original languageEnglish (US)
Article number115156
JournalPhysical Review B
Volume109
Issue number11
DOIs
StatePublished - Mar 15 2024

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