Optical conductivity of a metal near an Ising-nematic quantum critical point

Abstract

We study the optical conductivity of a pristine two-dimensional electron system near an Ising-nematic quantum critical point. We discuss the relation between the frequency scaling of the conductivity and the shape of the Fermi surface, namely, whether it is isotropic, convex, or concave. We confirm the cancellation of the leading order terms in the optical conductivity for the cases of isotropic and convex Fermi surfaces and show that the remaining contribution scales as $|\omega {|}^{2/3}$ at $T=0$. On the contrary, the leading term, $\propto |\omega {|}^{-2/3}$, survives for a concave FS. We also address the frequency dependence of the optical conductivity near the convex-to-concave transition. Explicit calculations are carried out for the Fermi-liquid regime using the modified (but equivalent to the original) version of the Kubo formula, while the quantum-critical regime is accessed by employing the space-time scaling of the $Z=3$ critical theory.

17 pages, 4 figures

References in corpus (6)

• Electrodynamics of Correlated Electron Materials
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Loop current fluctuations and quantum critical transport
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Quasiparticle scattering in a superconductor near a nematic critical point: resonance mode and multiple attractive channels

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• Fermi Liquid near a q=0 Charge Quantum Critical Point
• Quantum criticality and optical conductivity in a two-valley system
• Magnetoconductivity due to electron-electron interaction in a non-Galilean-invariant Fermi liquid
• Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal
• Strange metal at the Lifshitz transition
• Phonon Induced Energy Relaxation in Quantum Critical Metals