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Physical review. B, Condensed matter

Effects of Fermi-surface topology on the electronic properties of the two-dimensionalt-t’ model

Liang Chen, Pierre Bénard

Published Jul 1, 1995• 5 citations
Publisher

Abstract

We present a study of the two-dimensional t-t' model in the parameter regime of \ensuremath{\Vert}t'\ensuremath{\Vert}>\ensuremath{\Vert}t\ensuremath{\Vert}/2. As a function of band filling, the Fermi surface exhibits rich geometrical and topological properties, which have significant impact on the physical properties of the normal state. In particular, the Fermi surface becomes nested when the chemical potential reaches -${\mathit{t}}^{2}$/t', where the nesting vectors are [2 arccos(t/2t'),0] and [0,2 arccos(t/2t')]. The normal-state properties, such as the transport properties and charge and spin fluctuations, are analyzed in relation with the geometrical properties of the Fermi surface. We show that these properties lead to an optical charge-density wave mode within the random-phase approximation, even if the Hubbard interaction is repulsive. Implications for the recently introduced antiferromagnetic--van Hove model are also discussed.

DOI
10.1103/physrevb.52.1152

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We present a study of the two-dimensional t-t' model in the parameter regime of \ensuremath{\Vert}t'\ensuremath{\Vert}>\ensuremath{\Vert}t\ensuremath{\Vert}/2. As a function of band filling, the Fermi surface exhibits rich geometrical and topological properties, which have significant impact on the physical properties of the normal state. In particular, the Fermi surface becomes nested when the chemical potential reaches -t2{\mathit{t}}^{2}t2/t', where the nesting vectors are [2 arccos(t/2t'),0] and [0,2 arccos(t/2t')]. The normal-state properties, such as the transport properties and charge and spin fluctuations, are analyzed in relation with the geometrical properties of the Fermi surface. We show that these properties lead to an optical charge-density wave mode within the random-phase approximation, even if the Hubbard interaction is repulsive. Implications for the recently introduced antiferromagnetic--van Hove model are also discussed.
Possible Fermi-surface-related instabilities in a Hubbard model, generalized so as to include finite-range and exchange interactions, are studied in the weak-coupling limit. In addition to the usual instabilities of superconducting, charge- or spin-density-wave type, two new types of instability are found. The first state is an orbital antiferromagnet, with currents circulating around each elementary plaquette. In the second phase, a spin current flows around the plaquettes. In both cases, there are low-temperature power laws in thermodynamic and transport properties. Two-dimensional fluctuation effects are shown to lead, for weak interactions, to a sharp crossover from a Fermi-liquid state to a regime governed by orientational fluctuations of the order parameter at fixed amplitude.
We study the impact of the fermionic self-energy on one-loop functional renormalization group flows of the two-dimensional $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model, with emphasis on electronic densities away from van Hove filling. In the presence of antiferromagnetic hot spots, antiferromagnetic fluctuations lead to a flattening of the Fermi surface, shift magnetic phase boundaries, and significantly enhance critical scales. We trace back this effect to the presence of a magnetic first-order transition. For some parameters, the first-order character of the latter is reduced by self-energy effects. For reliably determining phase diagrams, the fermionic self-energy should be taken into account in functional renormalization group studies if scattering between hot spots is important.
The deformation of the Fermi surface induced by Coulomb interactions is investigated in the $t\ensuremath{-}{t}^{\ensuremath{'}}$-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that the interactions V enhance small anisotropies producing deformations of the Fermi surface that break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuk instability competes with magnetic instabilities and is suppressed at a critical value U(V).U(V).U(V). The interaction V effectively renormalizes the ${t}^{\ensuremath{'}}$ parameter to smaller values, which favors nesting. It also induces changes in the topology of the Fermi surface, which can go from holelike to electronlike. This may explain the results of recent angle-resolved photoemission spectroscopy experiments.
We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the (±π,0)(\pm π,0)(±π,0), (0,±π)(0,\pm π)(0,±π) regions as the normal state pseudogap observed in the high-TcT_cTc​ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around Q=(π,π){\bf Q}=(π,π)Q=(π,π) and the flatness of the band dispersion around the saddle point.
Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two-dimensional Hubbard model with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, we identify a line of Lifshitz transition points associated with a change in the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects and becomes more singular when ${t}^{\ensuremath{'}}$ becomes more negative. The resulting temperature dependence on the bare ddd-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at ${t}^{\ensuremath{'}}\ensuremath{\le}0$ extends our understanding of the quantum critical region in the phase diagram and shines lights on future investigations of the nature of the quantum critical point in the two-dimensional Hubbard model.