Abstract
The concept of Fermi liquid lays a solid cornerstone to the understanding of electronic correlations in quantum matter. This ordered many-body state rigorously organizes electrons at zero temperature in progressively higher momentum states, up to the Fermi surface. As such, it displays rigidity against perturbations. Such rigidity generates Fermi-surface resonances which manifest as longitudinal and transverse collective modes. Although these Fermi-liquid collective modes have been analyzed and observed in electrically neutral liquid helium, they remain unexplored in charged solid-state systems up to date. In this paper I analyze the transverse shear response of charged three-dimensional Fermi liquids as a function of temperature, excitation frequency and momentum, for interactions expressed in terms of the first symmetric Landau parameter. I consider the effect of momentum-conserving quasiparticle collisions and momentum-relaxing scattering in relaxation-time approximation on the coupling between photons and Fermi-surface collective modes, thus deriving the Fermi-liquid optical conductivity and dielectric function. In the high-frequency, long-wavelength excitation regime the electrodynamic response entails two coherent and frequency-degenerate polaritons, and its spatial nonlocality is encoded by a frequency- and interaction-dependent generalized shear modulus; in the opposite high-momentum low-frequency regime anomalous skin effect takes place. I identify observable signatures of propagating shear collective modes in optical spectroscopy experiments, with applications to the surface impedance and the optical transmission of thin films.
Highlights
The Fermi liquid represents a “Rosetta stone” for electronic correlations in weakly interacting electron systems
This condition allows for an effective hydrodynamic description of quasiparticle flow [9,10], whereby momentum and energy dissipation are encoded in the viscosity tensor [11], while dissipationless deformations of the fluid can be formulated in terms of “generalized elasticity” [9,12,13,14] and quantified by elastic moduli [9,15]
Eq (3) upon substituting ω2 → ω2 + iω/τK at the denominator. This expression is identical to the phenomenological dielectric function of viscous charged fluids with momentum damping [54] from microscopic Fermi-liquid theory: physically, the Fermi liquid macroscopically responds to shear stresses like a viscoelastic substance in the low-momentum, high-frequency regime
Summary
The Fermi liquid represents a “Rosetta stone” for electronic correlations in weakly interacting electron systems It translates (maps) the complexity of many-body interactions into a simpler description built in terms of nearly independent constituents, the electron-hole quasiparticles [1,2]. At higher energies hω > kBT Fermi-surface rigidity resists thermal fluctuations, so that one recovers substantial remnants of the T = 0 physics. All this wisdom is conventionally parametrized in terms of a quasiparticle collision time τc ∝ (hEF )/[(hω)2 + (kBT )2], stemming from the phase-space restriction for collision processes entailed by the Pauli principle [3,4]. There, if the collision time τc provides the smallest timescale in the
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
