arXiv:cond-mat/0612368 · Physical Review B

Self-energy corrections to anisotropic Fermi surfaces

Rafael Roldán, María P. López-Sancho, F. Guinea, Shan-Wen Tsai

Published Dec 13, 2006• 10 citations

Abstract

The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper-oxide superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is nontrivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.

DOI: 10.1103/physrevb.74.235109

Related papers

Deformation of anisotropic Fermi surfaces due to electron-electron interactions

Rafael Roldán, María P. López-Sancho, F. Guinea +1 more

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two-dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.

arXiv:cond-mat/0603673Europhysics Letters (EPL)Dec 1, 20062 citations

Anisotropic fermionic quasiparticles

Seongjin Ahn, S. Das Sarma

We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.

arXiv:2011.02481Physical review. B./Physical review. BJan 8, 20219 citations

Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model

Arne Neumayr, Walter Metzner

Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the noninteracting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical solutions of the self-consistency condition determining the Fermi surface and the gap function are calculated for the two-dimensional case. For the repulsive Hubbard model close to half-filling we find a superconducting state with d-wave symmetry, as expected. For Fermi levels close to the van Hove singularity a Pomeranchuk instability leads to Fermi surfaces with a broken square lattice symmetry, whose topology can be closed or open. For the attractive Hubbard model the second-order calculation yields an s-wave superconductivity with a weakly momentum dependent gap, whose size is reduced compared to the mean-field result.

arXiv:cond-mat/0208431Physical review. B, Condensed matterJan 21, 200397 citations

Deformation of the Fermi surface of a spinless two-dimensional electron gas in presence of an anisotropic Coulomb interaction potential

Orion Ciftja

We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree-Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.

Scientific ReportsFeb 4, 202114 citations

Spectral properties of two-dimensional Hubbard model with anisotropic hopping

V. Zlatić, P. Entel, S Grabowski

The zero-temperature spectral properties and Fermi surface (FS) anomalies of hole-doped 2D Hubbard model with anisotropic nearest-neighbor hopping are evaluated using the perturbation theory. The nested sections of the FS, which are always present in the anisotropic model, are found to expand with the strength of Coulomb correlation U. The renormalized FS and the low-energy part of the density of states obtained for small anisotropy and large U are similar to those obtained for large anisotropy and small U. The effect of correlation at low doping can best be described as an enhancement of the hopping anisotropy. The anomalous spectral features are mainly due to the van Hove singularities, which give rise to the momentum dependence of the self-energy.

Europhysics Letters (EPL)Jun 20, 199610 citations

Effects of spin fluctuations in the t-J model

Th. Obermeier, Thomas Pruschke, J. Keller

Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the t-J model. Solving the U = ∞ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction J are then included in a heuristical manner. Formally like in J-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. The obvious importance of antiferromagnetic (AF) correlations for the physics of cuprate superconductors found an impressing confirmation through ARUPS-experiments performed by Aebi et al. [1]. There, in a Fermi surface (FS) mapping of Bi2Sr2CaCu2O8(001) shadows of the FS were observed. The interpretation as an effect of short range antiferromagnetic correlations led to an intensive discussion of so called shadow features, which have been predicted by Kampf and Schrieffer [2] in a semi-phenomenological theory for the Hubbard model. In the paper we present an approximate evaluation of the self energy for the t-J model HtJ consisting of two parts: The hopping term Ht = − t∗

Jan 1, 19961 citation