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

Abstract

We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform ($\mathbf{Q}=0$) 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: $\Pi (\mathbf{q}=0,{\Omega }_m)\ne 0$. 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 $\Pi (\mathbf{q}=0,{\Omega }_m)\ne 0$ over a parametrically broad range of frequencies where the fermionic self-energy $\Sigma (\omega )$ is irrelevant, and use Eliashberg theory to compute $\Pi (\mathbf{q}=0,{\Omega }_m)$ in the non-Fermi liquid regime at smaller frequencies, where $\Sigma (\omega )>\omega$. We find that $\Pi (\mathbf{q}=0,\Omega )$ is a constant, plus a frequency dependent correction that goes as $|\Omega |$ at high frequencies, crossing over to $|\Omega {|}^{1/3}$ at lower frequencies. The $|\Omega {|}^{1/3}$ scaling holds also in a non-Fermi liquid regime. The non-vanishing of $\Pi (\mathbf{q}=0,\Omega )$ gives rise to additional structure in the imaginary part of the nematic susceptibility ${\chi }^{{}^{\prime \prime }}(\mathbf{q},\Omega )$ at $\Omega >v_{F}q$, 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.

References in corpus (8)

• Inelastic Light Scattering From Correlated Electrons
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• The key ingredients of the electronic structure of FeSe
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• A controlled expansion for certain non-Fermi liquid metals
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Critical behavior of itinerant fermions - role of finite size effects

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