Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
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PhysRevB.97.155115.pdf
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Author(s)
Klein, Avraham
Lederer, Samuel
Chowdhury, Debanjan
Berg, Erez
Chubukov, Andrey
Date Issued
April 2018
Journal
Physical Review B
Publisher
American Physical Society
Citation
Klein, Avraham et al. "Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter." Physical Review B 97, 15 (April 2018): 155115 © 2018 American Physical Society
Version
Final published version
Abstract
We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform (Q=0) Ising nematic quantum critical point of d-wave symmetry. The nematic order parameter is not a conserved quantity, and this permits a nonzero value of the fermionic polarization in the d-wave channel even for vanishing momentum and finite frequency: Π(q=0,Ω[subscript m])≠0. For weak coupling between the fermions and the nematic order parameter (i.e., the coupling is small compared to the Fermi energy), we perturbatively compute Π(q=0,Ω[subscript m])≠0 over a parametrically broad range of frequencies where the fermionic self-energy Σ(ω) is irrelevant, and use Eliashberg theory to compute Π(q=0,Ω[subscript m]) in the non-Fermi-liquid regime at smaller frequencies, where Σ(ω)>ω. We find that Π(q=0,Ω) is a constant, plus a frequency-dependent correction that goes as |Ω| at high frequencies, crossing over to |Ω|[superscript 1/3] at lower frequencies. The |Ω|[superscript 1/3] scaling holds also in a non-Fermi-liquid regime. The nonvanishing of Π(q=0,Ω) gives rise to additional structure in the imaginary part of the nematic susceptibility χ″(q,Ω) at Ω>v[subscript F]q, in marked contrast to the behavior of the susceptibility for a conserved order parameter. This additional structure may be detected in Raman scattering experiments in the d-wave geometry.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.97.155115
