Abstract:
The concept of quasiparticles is one of the cornerstones of the theory of quantum many-body systems. A growing number of recent experiments, however, have forced us to confront the existence of gapless quantum matter for which the concept of electronic quasiparticles does not apply. In the first part of this talk, I will consider the physics of a correlated mixed-valence insulator, where recent experiments have suggested the existence of an electrically insulating bulk hosting gapless fermionic excitations. In an effort to understand these paradoxical experiments, I will describe a new phase of matter--- the composite exciton Fermi liquid---which is an electrical insulator with a three-dimensional Fermi surface of neutral fermions. In the second part of the talk, inspired by the rich phenomenology of numerous non-Fermi liquid metals, I will construct concrete examples of solvable lattice models for non-Fermi liquids that do not admit a quasiparticle description but that nonetheless have a sharply-defined Fermi surface. Such an approach may help shine light on the universal aspects of a number of transport experiments in "strange" non-Fermi liquid metals. Finally, if time permits, I will present new experimental results on some unconventional transport properties of magic-angle twisted bilayer graphene and comment on their possible connections with the rest of my talk.