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arXiv:cond-mat/0109209 · Physical review. B, Condensed matter

Spectral functions, Fermi surface, and pseudogap in the t−J model

Peter Prelovšek, A. Ramšak

Published May 7, 2002• 35 citations
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Abstract

Spectral functions within the generalized $t\ensuremath{-}J$ model as relevant to cuprates are analyzed using the method of equations of motion for projected fermion operators. In the evaluation of the self-energy a decoupling of spin and single-particle fluctuations is performed. It is shown that in an undoped antiferromagnet the method reproduces the self-consistent Born approximation. For finite doping with short-range antiferromagnetic order the approximation evolves into a paramagnon contribution which retains a large incoherent contribution in the hole part of the spectral function as well as the hole-pocket-like Fermi surface at low doping. On the other hand, the contribution of longer-range spin fluctuations, with the coupling mostly determined predominantly by J and next-neighbor hopping ${t}^{\ensuremath{'}},$ is essential for the emergence of the pseudogap. The latter shows, at low doping in the effective truncation of the large Fermi surface, a reduced electron density of states and at the same time a quasiparticle density of states at the Fermi level.

DOI
10.1103/physrevb.65.174529

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Spectral functions within the generalized t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model as relevant to cuprates are analyzed using the method of equations of motion for projected fermion operators. In the evaluation of the self-energy a decoupling of spin and single-particle fluctuations is performed. It is shown that in an undoped antiferromagnet the method reproduces the self-consistent Born approximation. For finite doping with short-range antiferromagnetic order the approximation evolves into a paramagnon contribution which retains a large incoherent contribution in the hole part of the spectral function as well as the hole-pocket-like Fermi surface at low doping. On the other hand, the contribution of longer-range spin fluctuations, with the coupling mostly determined predominantly by J and next-neighbor hopping t\ensuremath′,{t}^{\ensuremath{'}},t\ensuremath′, is essential for the emergence of the pseudogap. The latter shows, at low doping in the effective truncation of the large Fermi surface, a reduced electron density of states and at the same time a quasiparticle density of states at the Fermi level.
The theoretical investigation of spectral functions and pseudogap in systems with strongly correlated electrons is discussed, with the emphasis on the single-band t-J model as relevant for superconducting cuprates. The evidence for the pseudogap features from numerical studies of the model is presented. One of the promising methods to study spectral functions is the method of equations of motion. The latter can deal systematically with the local constraints and projected fermion operators inherent for strongly correlated electrons. In the evaluation of the self energy the decoupling of spin and single-particle fluctuations is performed. In an undoped antiferromagnet the method reproduces the selfconsistent Born approximation (SCBA). For finite doping the approximation evolves into a paramagnon contribution which retains large incoherent contribution in the hole part. On the other hand, the contribution of longer-range spin fluctuations is essential for the emergence of the pseudogap. The latter shows up at low doping in the effective truncation of the large Fermi surface, reduced electron density of states and at the same time reduced quasiparticle density of states at the Fermi level.
Literature addressing the existence of ``hole pockets'' in experiments for the high-Tc{\mathrm{T}}_{\mathrm{c}}Tc​ cuprates and in theoretical analysis of electronic models of correlated electrons is reviewed. It is argued that the issue is not conclusively resolved, both in theory and experiments. The apparently large Fermi surface observed in numerical studies of the doped Hubbard and t-J models suggests the presence of 1-x carriers (with x the concentration of holes). However, this is in contradiction with results obtained in similar calculations for the Drude weight which scales with x at low doping. To address such a paradox, dressed operators are here used. Their spectral decomposition A(k,\ensuremath{\omega}) is analyzed specially using the t-J model on ladders, but considering also chains and two-dimensional (2D) clusters. The results are contrasted against those obtained with the standard bare operators. It is concluded that substantial changes in the spectral weight can occur by replacing the bare hole creation operator by its dressed version. Apparently large Fermi surfaces can turn into small ones by working with quasiparticle (qp) operators that represent accurately the state of one hole. Thus, large Fermi surfaces in angle-resolved photoemission (ARPES), obtained by the sudden removal of an electron, may not be in contradiction with a visualization of the normal state of lightly doped antiferromagnets as composed of a gas of spin polarons with energies approximately obtained from the rigid band doping of the half-filled dispersion. The coexistence of a large Fermi surface in ARPES with, e.g., a holelike Hall coefficient seems possible in systems with strong correlations. In this paper the expression ``hole pocket'' is used as representing a large accumulation of spectral weight centered at k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) generated by antiferromagnetic correlations in 2D clusters, or in analogous positions for ladders and chains. The subtle issue of whether such hole pockets represent a true small Fermi surface or just large incoherent weight cannot be addressed with finite resolution techniques such as angle-resolved photoemission and numerical studies of electronic models. They only provide information about the location of the dominant weight in A(k,\ensuremath{\omega}). The ideas discussed here are very general and they can be applied to a variety of problems where quasiparticles are strongly dressed by low energy excitations of the medium in which they are immersed.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation n T and temperature is calculated. At low temperatures, the susceptibility presents a peak for n T ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above n T ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
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.
We compute high-resolution angle-resolved photoemission spectroscopy of the Hubbard model using the unbiased determinant quantum Monte Carlo algorithm, revealing an asymmetry between electron and hole doping. Electron doping exhibits more coherent quasiparticles and stronger antiferromagnetic correlations compared to hole doping. At low doping, a nodal-antinodal dichotomy on the Fermi surface is observed, similar to cuprate experiments. The dichotomy reflects the momentum dependence of the Mott gap, as manifested in both the spectral function and the self-energy. For hole doping, we observe a transition towards the pseudogap, without signature of pocket formation. The simulated nuclear magnetic resonance pseudogap temperatures do not necessarily agree with the temperature determined by spectroscopy. These findings collectively suggest the pseudogap is a smooth crossover driven by strong correlations.