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Electron self-energy near a nematic quantum critical point

Markus Garst and Andrey V. Chubukov
Phys. Rev. B 81, 235105 – Published 7 June 2010

Abstract

We consider an isotropic Fermi liquid in two dimensions near the n=2 Pomeranchuk instability in the charge channel. The order parameter is a quadrupolar stress tensor with two bosonic shear modes with polarizations longitudinal and transverse to the quadrupolar momentum tensor. Longitudinal and transverse bosonic modes are characterized by dynamical exponents z=3 and z=2, respectively. Previous studies have found that such a system exhibits multiscale quantum criticality with two different energy scales ωξz,, where ξ is the correlation length. We study the impact of the multiple energy scales on the electron Green’s function. The interaction with the critical z=3 mode is known to give rise to a local self-energy that develops a non-Fermi-liquid form, Σ(ω)ω2/3 for frequencies larger than the energy scale ωξ3. We find that the exchange of transverse z=2 fluctuations leads to logarithmically singular renormalizations of the quasiparticle residue Z and the vertex Γ. We derive and solve renormalization-group equations for the flow of Z and Γ, and show that the system develops an anomalous dimension at the nematic quantum critical point (QCP). As a result, the spectral function at a fixed ω and varying k has a non-Lorentzian form. Away from the QCP, we find that the flow of Z is cut at the energy scale ωFLξ1, associated with the z=1 dynamics of electrons. The z=2 energy scale, ωξ2, affects the flow of Z only if one includes into the theory self-interaction of transverse fluctuations.

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  • Received 12 March 2010

DOI:https://doi.org/10.1103/PhysRevB.81.235105

©2010 American Physical Society

Authors & Affiliations

Markus Garst1,2 and Andrey V. Chubukov3

  • 1Institut fur Theoretische Physik, Universität zu Köln, 50937 Köln, Germany
  • 2Physik Department, Technische Universität München, 85748 Garching, Germany
  • 3Department of Physics, University of Wisconsin–Madison, 1150 University Avenue, Madison, Wisconsin 53706-1390, USA

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Issue

Vol. 81, Iss. 23 — 15 June 2010

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