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arXiv:cond-mat/0003278 · Physical Review Letters

Spontaneous Deformation of the Fermi Surface due to Strong Correlation in the Two-Dimensional t - J Model

Akihiro Himeda, Masao Ogata

Published Nov 13, 2000• 48 citations
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Abstract

The Fermi surface of the two-dimensional t- J model is studied using the variational Monte Carlo method. We study the Gutzwiller-projected d-wave superconducting state with an additional variational parameter t(')(v) corresponding to the next-nearest-neighbor hopping term. It is found that the finite t(')(v)<0 gives the lowest variational energy in the wide range of hole-doping rates. The obtained momentum distribution function shows that the Fermi surface deforms spontaneously. It is also shown that the Van Hove singularity is always located very close to the Fermi energy. Using the Gutzwiller approximation, we show that this deformation is due to the Gutzwiller projection operator or the strong correlation.

DOI
10.1103/physrevlett.85.4345

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The Fermi surface of the two-dimensional t- J model is studied using the variational Monte Carlo method. We study the Gutzwiller-projected d-wave superconducting state with an additional variational parameter t(')(v) corresponding to the next-nearest-neighbor hopping term. It is found that the finite t(')(v)<0 gives the lowest variational energy in the wide range of hole-doping rates. The obtained momentum distribution function shows that the Fermi surface deforms spontaneously. It is also shown that the Van Hove singularity is always located very close to the Fermi energy. Using the Gutzwiller approximation, we show that this deformation is due to the Gutzwiller projection operator or the strong correlation.
In this paper, the effect of the next-earest (t ′ ) and third-earest (t ′ ′ ) hopping terms on superconductivity (SC) of the two-dimensional (2D) extended t-J model is studied by the variational Monte-Carlo (VMC) method. For hole-doped systems, the d-wave pairing correlation is suppressed by t ′ and t ′ ′ for underdoped cases, while it can be greatly enhanced by proper values of t ′ and t ′ ′ for the overdoped ones. This behavior results from the deformation of the Fermi surfaces. PACS numbers: 74.20.-z, 71.18.+y The 2D t-J model is one of the most popular models for studying the properties of the high-temperature superconductivity (HTS) [1, 2]. Yet the problem whether this model can give such high Tc for the cuprates or not is still under debate [4–7]. It has been well accepted that the next-nearest-neighbor (t ′ ) and the third-nearest-neighbor (t ′ ′) hopping terms are necessary for models to explain several experiments like angle-resolved photoemission (ARPES) of HTS [3]. However, the effect of t ′ and t ′ ′ on pairing correlation is also controversial. Previous DMRG studies of the two-dimensional (2D) extended t-J model show that the SC is suppressed (enhanced) for negative (positive) next-nearestneighbor hopping t ′ /t [8]. But results from first-principle calculation show that t ′ /t = −0.3 maximizes SC at optimal doping [9]. The Hamiltonian of the extended t-J model is H = Ht + HJ = − ∑ ij tij(˜c † i,σ ˜cj,σ + H.C.) + J ∑
We perform a variational Monte Carlo study on spontaneous d-wave form Fermi surface deformation (dddFSD) within the three-band Hubbard model. It is found that the variational energy of a projected Fermi sea is lowered by introducing an anisotropy between the hopping integrals along the x and y directions. Our results show that the dddFSD state has the strongest tendency at half-filling in the absence of magnetism, and disappears as the hole concentration increases to nh≈1.15n_h\approx 1.15nh​≈1.15. This is qualitatively in agreement with the mean field analysis and the exact diagonalization calculation for the one-band models, and provides a qualitative explanation to the "intra-unit-cell" electronic nematicity revealed by the scanning tunneling microscopy. An analysis of the dependence of dddFSD on the parameters of the three-band model indicates that the copper on-site Coulomb interaction, the nearest-neighbor copper-oxygen repulsion, and the charge-transfer energy have a remarkable positive effect on dddFSD.
A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t – J model with the hopping electron amplitudes t (and ) between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the methodʼs results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed 'grand-canonical Gutzwiller approximation' (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the doping dependence of the gap magnitude with experimental data. Fourth, we analyze the k -space properties of the model: Fermi surface topology and effective dispersion. The DE-GWF method opens up new perspectives for studying strongly correlated systems, as it (i) works in the thermodynamic limit, (ii) is comparable in accuracy to VMC, and (iii) has numerical complexity comparable to that of the GA (i.e., it provides the results much faster than the VMC approach).
We have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first- and second-neighbor hopping terms in order to study the coexistence state of a static stripe state and a modulated d-wave superconductivity in the underdoped cuprates. In addition to a Gutzwiller, a Jastrow and a doublon-holon correlation effects, the band-renormalization effect was considered in the trial wave function. The condensation energies of an 8-period stripe state was computed as a function of a Coulomb energy under the hole-density x=1/8. Our results reveal that the renormalization of higher hopping parameters due to the strong correlation effect enhances the one-dimensional hole motion on a quarter-filled band in the stripe state, and brings quasi-Fermi surface close to the magnetic zone boundary in the coexistence state.
A variational Monte Carlo calculation is used for studying the ground state of the two-dimensional Hubbard model, including hopping between both nearest and next-nearest neighbor sites. Superconductivity with d-wave symmetry is found to be restricted to densities where the Fermi surface crosses the magnetic zone boundary. The condensate energy is much larger for hole doping than for electron doping. Superconductivity is kinetic energy driven for hole doping, but potential energy driven for electron doping. Our findings agree surprisingly well with experimental data for layered cuprates, both for electron- and hole-doped materials.
The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.