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arXiv:0804.4422 · Physical Review B

Fermi liquid instabilities in two-dimensional lattice models

Carlos Alberto Lamas, D. C. Cabra, Nicolás Grandi

Published Sep 4, 2008• 26 citations
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Abstract

We develop a procedure for detecting Fermi liquid instabilities by extending the analysis of Pomeranchuk to two-dimensional lattice systems. The method is very general and straightforward to apply, thus, provides a powerful tool for the search of exotic phases. We test it by applying it to a lattice electron model with interactions leading to $s$- and $d$-wave instabilities.

DOI
10.1103/physrevb.78.115104

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We develop a procedure for detecting Fermi liquid instabilities by extending the analysis of Pomeranchuk to two-dimensional lattice systems. The method is very general and straightforward to apply, thus, provides a powerful tool for the search of exotic phases. We test it by applying it to a lattice electron model with interactions leading to sss- and ddd-wave instabilities.
In the present paper we extend the method to detect Pomeranchuk instabilities in lattice systems developed in previous works to study more general situations. The main result presented here is the extension of the method to include finite temperature effects, which allows to compute critical temperatures as a function of interaction strengths and density of carriers. Furthermore, it can be applied to multiband problems which would be relevant to study systems with spin/color degrees of freedom. Altogether, the present extended version provides a potentially powerful technique to investigate microscopic realistic models relevant to e.g. the Fermi liquid to nematic transition extensively studied in connection with different materials such as cuprates, ruthenates, etc.
In the present paper we extend the method to detect Pomeranchuk instabilities in lattice systems developed in previous works to study more general situations. The main result presented here is the extension of the method to include finite temperature effects, which allows to compute critical temperatures as a function of interaction strengths and density of carriers. Furthermore, it can be applied to multiband problems which would be relevant to study systems with spin/color degrees of freedom. Altogether, the present extended version provides a potentially powerful technique to investigate microscopic realistic models relevant to the Fermi liquid to nematic transition extensively studied in connection with different materials such as cuprates, ruthenates, etc.
We study the effects of spin-antisymmetric interactions on the stability of a Landau–Fermi liquid on the square lattice, using the generalized Pomeranchuk method for two-dimensional lattice systems. In particular, we analyze interactions that could induce instabilities of the so-called spin-split type, that is when spin-up and spin-down Fermi surfaces are displaced with respect to each other. The phase space is studied as a function of the strength of the interaction V, the electron chemical potential μ and an external magnetic field h. We find that such interactions produce in general an enhancement of the instability region of the Landau–Fermi liquid. More interestingly, in certain regions of the V–μ phase space, we find a reentrant behavior as a function of the magnetic field h, similar to that found in recent experiments, e.g. in URu₂Si₂ and Sr₃Ru₂O₇.
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.
Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.
In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion Fl{F}_{l}Fl​ $\ensuremath{\ge}$ −1-1−1. Interestingly, charge and spin conservation prevent interactions from destabilizing the lll=1 channel even when Fl{F}_{l}Fl​ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing lll=1 instabilities. Then, they construct lll=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.