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arXiv:cond-mat/9804153

Phase Diagram of High-T_c Superconductors from a Field Theory Model

Jose Vicente Alvarez, J. González, F. Guinea, María A. H. Vozmediano

Published Apr 15, 1998• 0 citations
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Abstract

The renormalization group approach to correlated fermions is used to determine the phase diagram of the oxide cuprates modeled by the t-t' Hubbard model at the Van Hove filling. Spin-dependent interactions give rise to instabilities corresponding to ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space.

DOI
10.48550/arxiv.cond-mat/9804153

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The renormalization group approach to correlated fermions is used to determine the phase diagram of the oxide cuprates modeled by the t-t' Hubbard model at the Van Hove filling. Spin-dependent interactions give rise to instabilities corresponding to ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space.
Phase diagrams of the two-dimensional one-band $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model are obtained within the two-patch and temperature-cutoff many-patch renormalization group approaches. At small ${t}^{\ensuremath{'}}$ and at van Hove band fillings antiferromagnetism dominates, while with increasing ${t}^{\ensuremath{'}}$ or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near ${t}^{\ensuremath{'}}=t/2$ and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.
The phase diagram of the two-dimensional extended one-band $U\ensuremath{-}V\ensuremath{-}J$ Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization-group (RG) approaches near the Van Hove band fillings. At small ${t}^{\ensuremath{'}}$ and J>0,J>0,J>0, mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach that predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. There is a complex competition between SDW, CF phases, and d-wave superconductivity at small ${t}^{\ensuremath{'}}$ in two- and many-patch RG approaches. The spin-flux phase, which is not stable at the mean-field level, is identified as a possible ground state at J<0J<0J<0 in both RG approaches. With increasing ${t}^{\ensuremath{'}}$ the results of all three approaches merge: d-wave superconductivity at J>0J>0J>0 and ferromagnetism at J<0J<0J<0 become the leading instabilities. For large enough V, the charge-density-wave state occurs.
Perturbative corrections to the mean field theory for particle-hole instabilities of interacting electron systems are computed within a scheme which is equivalent to the recently developed variational approach to the Kohn-Luttinger superconductivity. This enables an unbiased comparison of particle-particle and particle-hole instabilities within the same approximation scheme. A spin-rotation invariant formulation for the particle-hole instabilities in the triplet channel is developed. The method is applied to the phase diagram of the t-t' Hubbard model on the square lattice. At the Van Hove density, antiferromagnetic and d-wave Pomeranchuk phases are found to be stable close to half filling. However, the latter phase is confined to an extremely narrow interval of densities and away from the singular filling, d-wave superconducting instability dominates.
We investigate the phase diagram of two-dimensional (2D) Hubbard model by employing the optimization variational Monte Carlo method. The 2D Hubbard model is the most simple electronic model for cuprate high-temperature superconductors. The phase diagram consists of three regions; they are antiferromagnetic insulator (AFI) region, superconducting (SC) region and the coexistent region of superconductivity and antiferromgantism. The phase diagram obtained by numerical calculations well agrees with the experimental phase diagram for high-temperature cuprates. We mainly focused on the effect of t′t't′ on the antiferromagnetic (AF) correlation and the AFI region. The area of the AF phase increases when we include t′t't′ and thus the pure ddd-wave SC phase decreases. The AFI phase near half filling decreases as ∣t′∣|t'|∣t′∣ increases.
A systematic study is made of the t-J model as a working model for copper oxide high-Tc superconductors. The main focus is on the near-half- filling region (low hole concentrations) relevant to these materials. The theory of the magnetic polaron, which is a charge carrier traveling in an antiferromagnetic matrix, and the theory of antiferromagnetic ordering are discussed in a unified framework. The spin liquid state beyond the antiferromagnetic phase is examined. The Hamiltonian parameters – hole concentration phase diagram for the model is described and compared with that for the Hubbard model in the strong correlation limit. Two extensions of the t-J model, the t-t'-J model and the three-center interaction model, are discussed. Mostly analityc strong correlation techniques are employed in this review.