Correlated metals, and sometimes insulators, often display non-Fermi liquid properties, e.g., single-particle spectra lacking quasiparticles and metallic charge transport being poor or absent, coexisting with conventional Fermi liquid behaviour, e.g., in thermal properties or in quantum oscillations. This Janus-faced character likely entails the existence of new paradigms of strongly interacting electrons, but it might simply indicate that the class of Landau’s Fermi liquids is broader and richer than commonly believed.
I will show that contrary to common belief, coherent 'quasiparticles' also emerge approaching a Luttinger surface, i.e., the location within the Brillouin zone of the zeros of the single-particle Green’s function at zero energy and temperature, just as they do approaching a Fermi surface, where the Green's function instead has poles. This occurs despite the single-particle pseudogap at the Luttinger surface. The microscopic derivation of Fermi liquid theory and its conventional linear response and thermodynamic susceptibilities work also for 'quasiparticles' at a Luttinger surface: for instance, they yield a standard linear in temperature specific heat, in striking contrast with the vanishing single-particle density of states. Remarkably, the correct use of Luttinger’s theorem when perturbation theory breaks down, such as due to a Luttinger surface, shows that the number of 'quasiparticles' at a Luttinger surface counts the number of physical holes, while the number of quasiparticles at the Fermi surface counts the number of physical electrons.
I will discuss the surprisingly rich physics coming out of a toy self-energy inspired by the phenomenology of underdoped cuprates, and which admits a Luttinger surface either alone or coexisting with Fermi pockets, and thus unconventional 'quasiparticles' coexisting or not with conventional ones.
M. Fabrizio, arXiv:2105.12528; M. Fabrizio, PRB 102, 155122 (2020).