TY - JOUR

T1 - Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter

AU - Klein, Avraham

AU - Lederer, Samuel

AU - Chowdhury, Debanjan

AU - Berg, Erez

AU - Chubukov, Andrey

N1 - Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/4/9

Y1 - 2018/4/9

N2 - 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,Ωm)≠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,Ωm)≠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,Ωm) 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|1/3 at lower frequencies. The |Ω|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>vFq, 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.

AB - 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,Ωm)≠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,Ωm)≠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,Ωm) 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|1/3 at lower frequencies. The |Ω|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>vFq, 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.

UR - http://www.scopus.com/inward/record.url?scp=85045221639&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.97.155115

DO - 10.1103/PhysRevB.97.155115

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AN - SCOPUS:85045221639

SN - 2469-9950

VL - 97

JO - Physical Review B

JF - Physical Review B

IS - 15

M1 - 155115

ER -