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arXiv:cond-mat/0205597

Superconductivity and Instabilities in the t-t' Hubbard Model

Franz Wegner, V. Hankevych

Published May 28, 2002• 1 citation
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Abstract

We present a stability analysis of the 2D t-t' Hubbard model on a square lattice for t' = -t/6. We find possible phases of the model (d-wave Pomeranchuk and superconducting states, band splitting, singlet and triplet flux phases), and study the interplay of them.
DOI
10.48550/arxiv.cond-mat/0205597

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We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.
We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.
In connection with the symmetry-breaking phenomena found in cuprate superconductors, the instability toward x-y and (x + y)-(xy) anisotropy (Pomeranchuk instability) is studied for a strongly correlated Hubbard model (U/t = 12) on a square lattice with the next-nearest-neighbor transfer t ′ , using a variational Monte Carlo method.By analyzing a normal (paramagnetic), d x 2 -y 2 -wave superconducting, and antiferromagnetic states for t ′ /t = 0, ±0.3 and 0 ≤ δ ≤ 0.3 (δ: doping rate), we argue that the possibility of Pomeranchuk instability is limited to the normal state with t ′ /t = 0 and 0.05 ≲ δ ≲ 0.20 in the x-y anisotropy.Band-renormalization effects (Fermi-surface changes), which are introduced to each state, play a crucial role for the argument.