NEW COLLECTIVE MODE AND CORRECTIONS TO FERMI-LIQUID THEORY IN 2 DIMENSIONS

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<2kF, 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 5/2 correction to (kF,) is obtained. The 2D case is also contrasted with a similar calculation in 1D. © 1990 The American Physical Society.