Effect of singular interaction terms on two-dimensional Fermi liquids.

Abstract

The structure of perturbation theory for an interacting two-dimensional Fermi system is analyzed, in the case where singular terms exist in the quasiparticle interactions. These give a hierarchy of singular terms in the one-particle self-energy. The dominant terms are self-consistently summed, to give a quasiparticle pole vanishing as Z(\ensuremath{\omega})\ensuremath{\sim}(\ensuremath{\omega}/${\mathrm{\ensuremath{\omega}}}_{0}$${)}_{0}^{\mathrm{\ensuremath{\rho}},\mathrm{\ensuremath{\delta}}2}$/${\mathrm{\ensuremath{\Elzxh}}}^{2}$N(0)${\mathrm{\ensuremath{\omega}}}_{0}$ near the Fermi energy (signaling a breakdown of Fermi-liquid theory), and a form for the scattering amplitude which is consistent with the assumed form for the quasiparticle interaction.