Kohn-Luttinger effect in nested fermion liquids
Physical Review B (Condensed Matter)
We study the Kohn-Luttinger effect in a two-dimensional (2D) nested Fermion liquid with a repulsive interaction via the renormalization group method and identify the resulting order parameter symmetry. Using the band structure of the 2D Hubbard model close to half-filling as a prototype, we construct an effective low-energy theory. We use multidimensional bosonization to incorporate the zero-sound channel and find marginal Fermi liquid behavior in the absence of any instability. We show an
... g of the Landau theorem in nested Fermion liquids, which serves as the criterion of the BCS instability. Including repulsive or antiferromagnetic exchange interactions in the low-energy theory, we show that the d_x^2-y^2-wave BCS channel is renormalized to be the most attractive. Below half-filling, when the nesting is not perfect, there is competition between the spin-density-wave (SDW) and the BCS channels; when the SDW coupling is small enough, there occurs a d_x^2-y^2-wave superconducting instability at sufficiently low temperatures.