Weak coupling instabilities of two-dimensional lattice electrons

Abstract

We present a consistent and systematic study of a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high-energy spin fluctuations create an effective attraction between the quasi-particles. However in the special case of a half-filled nearest-neighbor tight-binding band, the Fermi surface is nested and the system is at a Van Hove singularity. In this situation, there are six competing instabilities: s- and d-wave superconductivity, spin- and charge-density waves and two phases with circulating charge and spin currents, respectively. The required renormalization group formalism can be presented on a most elementary level, connecting the idea of the “parquet summation” to the more modern concept of Wilson's effective action. As a result, a rich phase diagram is obtained as a function of the model interaction. We also argue that the one-loop approximation is insufficient in a case where the Fermi surface is at a Van Hove singularity but not nested.