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The concept of Fermi liquid lays a solid cornerstone to the understanding ofelectronic correlations in quantum matter. This ordered many-body staterigorously organizes electrons at zero temperature in progressively highermomentum states, up to the Fermi surface. As such, it displays rigidity againstperturbations. Such rigidity generates Fermi-surface resonances which manifestas longitudinal and transverse collective modes. Although these Fermi-liquidcollective modes have been analyzed and observed in electrically neutral liquidhelium, they remain unexplored in charged solid-state systems up to date. Inthis paper I analyze the transverse shear response of charged three-dimensionalFermi liquids as a function of temperature, excitation frequency and momentum,for interactions expressed in terms of the first symmetric Landau parameter. Iconsider the effect of momentum-conserving quasiparticle collisions andmomentum-relaxing scattering in relaxation-time approximation on the couplingbetween photons and Fermi-surface collective modes, thus deriving theFermi-liquid optical conductivity and dielectric function. In thehigh-frequency, long-wavelength excitation regime the electrodynamic responseentails two coherent and frequency-degenerate polaritons, and its spatialnonlocality is encoded by a frequency- and interaction-dependent generalizedshear modulus; in the opposite high-momentum low-frequency regime anomalousskin effect takes place. I identify observable signatures of propagating shearcollective modes in optical spectroscopy experiments, with applications to thesurface impedance and the optical transmission of thin films.

Optical signatures of shear collective modes in strongly interacting Fermi liquids