New collective mode and corrections to Fermi-liquid theory in two dimensions

Abstract

We study a two-dimensional Fermi gas with an arbitrary short-range repulsive interaction. We show that the vertex part has an unusual singularity in the particle-particle channel for all momenta q${\mathit{k}}_{\mathit{F}}$, which is not found in higher dimensions. We interpret this as a collective mode representing a bound excitation of two holes. This mode, however, does not lead to an instability, or to a breakdown of Fermi-liquid theory in the low-density limit. The resulting Fermi-surface phase shift vanishes, and a ‖ω${\mathrm{\Vert }}^{5/2}$ correction to Σ’ ’(${\mathit{k}}_{\mathit{F}}$,ω) is obtained. The 2D case is also contrasted with a similar calculation in 1D.