Quasiparticle lifetimes in two-dimensional Fermi liquids

With recent experimental advances in the creation of ultraclean two-dimensional materials and the observation of interaction-dominated electron transport, there is now a renewed interest in the seemingly well-understood topic of interacting Fermi liquids. In particular, it has been proposed that two-dimensional Fermi liquids admit two distinct and vastly separate characteristic lifetimes: While even-parity perturbations of the Fermi surface decay with the standard Fermi-liquid quadratic temperature scaling, odd-parity perturbations are predicted to decay much more slowly. This raises the tantalizing prospect of a novel Fermi liquid transport regime in which odd modes are collisionless but even modes are collision-dominated (i.e., hydrodynamic). We confirm this picture by developing a systematic basis expansion for the linearized Fermi-liquid collision integral valid at all temperatures, which not only provides a comprehensive description of the degenerate low-temperature regime but also encompass the high-temperature expansion of a classical gas. We compute the eigenvalues of the linearized collision integral, which set the quasiparticle decay rates, for the first 20 angular harmonics of the quasiparticle perturbation down to ultralow temperatures T/T_F = 10^{-5} and establish that odd-parity excitations cross over from a diffusive quadratic scaling at low temperatures to a new subdiffusive scaling with quartic temperature dependence at ultralow temperatures. Our work demonstrates that the crossover temperature to this new transport regime is a sizeable fraction of the Fermi temperatures and thus experimentally accessible. Moreover, the formalism we have developed can be used for general solutions of the Fermi liquid transport equations.