Abstract

The phenomenology of Fermi liquids describes the properties of conduction electrons in many metals in terms of weakly-interacting quasiparticles. The resulting charged quantum liquid sustains different kinds of collective excitations, due to residual interactions and collisions between quasiparticles. External perturbation potentials, like an oscillating electric field, can excite these collective modes, generating a coherent oscillation of quasiparticles at the Fermi surface. In particular, long-wavelength perturbations at local equilibrium allow for a description of collective modes in terms of generalized elasticity, whereby the Fermi surface oscillation is analogous to the vibration of a viscoelastic medium. An example of such perturbations is given by electromagnetic waves, which excite a transverse response of the Fermi liquid involving a shear elastic and a shear viscous component. This way, one can use electromagnetic radiation to probe long-wavelength transverse collective modes in Fermi liquids [1]. Using this viscoelastic model, we show that the presence of collective modes has significant consequences on the interaction of radiation with the Fermi liquid: two distinct frequency-degenerate optical modes exist, one of them showing negative refraction at sufficiently low frequency and low quasiparticle collision rate. These optical modes interfere coherently along their propagation in space, giving rise to standing wave patterns. Such effects can leave observable consequences on optical spectroscopy experiments in metallic samples at low temperatures. As archetype examples, we consider the optical transmission and reflection of radiation through semi-infinite systems and slabs, and the surface impedance.

[1] D. Forcella, J. Zaanen, D. Valentinis and D. van der Marel, Phys. Rev B 90, 035143 (2014)