Dynamical susceptibility of a Fermi liquid

Abstract

We study the dynamic response of a Fermi liquid in the spin, charge and nematic channels beyond the random phase approximation for the dynamically screened Coulomb potential. In all the channels, one-loop order corrections to the irreducible susceptibility result in a non-zero spectral weight of the corresponding fluctuations above the particle-hole continuum boundary. It is shown that the imaginary part of the spin susceptibility, $\text{Im}{\chi }_s(\mathbf{q},\omega )$, falls off as $q^2/\omega$ for frequencies above the continuum boundary ($\omega \gg v_{F}q$) and below the model-dependent cutoff frequency, whereas the imaginary part of the charge susceptibility, $\text{Im}{\chi }_c(\mathbf{q},\omega )$, falls off as $(q/k_F{)}^2{q}^2/\omega$ for frequencies above the plasma frequency. An extra factor of $(q/k_F{)}^2$ in $\text{Im}{\chi }_c(\mathbf{q},\omega )$ as compared to $\text{Im}{\chi }_s(\mathbf{q},\omega )$ is a direct consequence of Galilean invariance. The imaginary part of the nematic susceptibility increases linearly with $\omega$ up to a peak at the ultraviolet energy scale-- the plasma frequency and/or Fermi energy--and then decreases with $\omega$. We also obtain explicit forms of the spin susceptibility from the kinetic equation in the collisionless limit and for the Landau function that contains up to first three harmonics.

arXiv comment25 pages, 7 figures

References in corpus (24)

• Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
• Inelastic Light Scattering From Correlated Electrons
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Quantum Theory of a Nematic Fermi Fluid
• Gauge-invariant response functions of fermions coupled to a gauge field
• Coulomb Drag in Normal Metals and Superconductors: Diagrammatic Approach
• Nonanalytic behavior of the spin susceptibility in clean Fermi systems
• Dynamic response of one-dimensional interacting fermions
• Anomalous density fluctuations in a strange metal
• Interaction corrections to the polarization function of graphene
• Optical response of correlated electron systems
• Hyperscaling violation at the Ising-nematic quantum critical point in two dimensional metals
• Spin susceptibility of interacting two-dimensional electrons in the presence of spin-orbit coupling
• Plasmon attenuation and optical conductivity of a two-dimensional electron gas
• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
• Ferromagnetic order of nuclear spins coupled to conduction electrons: a combined effect of the electron-electron and spin-orbit interactions
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation
• The Conditions for $l=1$ Pomeranchuk Instability in a Fermi Liquid
• Spin-independent effective mass in a valley-degenerate electron system
• Universal and non-universal renormalizations in Fermi liquids
• Gradient terms in quantum-critical theories of itinerant fermions
• Dynamical spin structure factor of one-dimensional interacting fermions

Cited by in corpus (7)

• Collective modes near a Pomeranchuk instability
• Collective spinon spin wave in a magnetized U(1) spin liquid
• Exceptional points in Fermi liquids with quadrupolar interactions
• Drag viscosity of metals and its connection to Coulomb drag
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Optical conductivity of a Dirac-Fermi liquid
• Intertwined geometries in collective modes of two dimensional Dirac fermions