Journal article

Weak coupling instabilities of two-dimensional lattice electrons

  • Binz, Benedikt Department of Physics, Fribourg University, Switzerland - Theoretische Physik, ETH Zürich, Switzerland
  • Baeriswyl, Dionys Department of Physics, Fribourg University, Switzerland
  • Douçot, B. Laboratoire de Physique Théorique et Hautes Energies, CNRS Universités Paris VII, France
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  • Physica C: Superconductivity. - 2004, vol. 408-410, no. 250-251
English 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.
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