TY - JOUR

T1 - Electron self-energy near a nematic quantum critical point

AU - Garst, Markus

AU - Chubukov, Andrey V.

PY - 2010/6/7

Y1 - 2010/6/7

N2 - 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 ω∼ ξ-z∥,⊥, 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 ω∼ ξ-3. 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 ωFL ∝ ξ-1, associated with the z=1 dynamics of electrons. The z⊥ =2 energy scale, ω∼ ξ-2, affects the flow of Z only if one includes into the theory self-interaction of transverse fluctuations.

AB - 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 ω∼ ξ-z∥,⊥, 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 ω∼ ξ-3. 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 ωFL ∝ ξ-1, associated with the z=1 dynamics of electrons. The z⊥ =2 energy scale, ω∼ ξ-2, affects the flow of Z only if one includes into the theory self-interaction of transverse fluctuations.

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U2 - 10.1103/PhysRevB.81.235105

DO - 10.1103/PhysRevB.81.235105

M3 - Article

AN - SCOPUS:77956332227

SN - 1098-0121

VL - 81

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 23

M1 - 235105

ER -