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Journal of Physics Condensed Matter

Real-space electron pairing in two-dimensional systems

Chumín Wang, Oracio Navarro

Published Aug 16, 1993• 0 citations
Publisher

Abstract

The local-pairing problem of two electrons with parallel and anti-parallel spins is analysed by looking at the pairing energy, the coherence length and the mobility of pairs in a square lattice. These physical quantities are calculated by a novel method based on mapping the Hubbard problem onto a tight-binding one in a higher-dimensional space, which can be solved exactly.

DOI
10.1088/0953-8984/5/33a/060

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The local-pairing problem of two electrons with parallel and anti-parallel spins is analysed by looking at the pairing energy, the coherence length and the mobility of pairs in a square lattice. These physical quantities are calculated by a novel method based on mapping the Hubbard problem onto a tight-binding one in a higher-dimensional space, which can be solved exactly.
In this work we solve a general Hubbard Hamiltonian for two interacting particles in a periodic and nonperiodic infinite one-dimensional lattice, using a real-space mapping method, the renormalized perturbation expansion (RPE), and the Green-function technique. This Hamiltonian considers a general bond-charge interaction, the on-site interaction, and the general intersite interaction. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding problem in a higher-dimensional space. Analyzing the periodic and the quasiperiodic lattices in this new space, we obtained the analytical solution for the binding condition at the ground state. Our general results for the periodic chain reproduce completely the limit cases of the numerical solution obtained previously and those obtained in reciprocal space
In this paper we report a novel method to find the exact solution oC the extended lIubbard lIamiltonian. This method is based on mapping the original problem onto a tight-binding probJem in a higher dimensional space, which has exact solution. For one- and two-dimensional systems with a low electronic density, we have calculated the electronic pairing energy and the coherence length Cor different interaction regimes. This study can be extended to analyze the electronie correlation in non-periodic systems.
The electron pairing problem is studied by means of the extended Hubbard Hamiltonian. The original many-body problem is mapped onto a tight-binding one in a higher dimensional space, where the problem can be solved in an exact way. In a triangular lattice, the effects of the frustration of antibonding states on the electronic correlation are analyzed in detail. It is found that the hole pairing is always stronger than the electron case, in contrast with the bipartite lattices, where there is a complete symmetry between electron and hole pairings. The ground state of two holes, when the attractive nearest-neighbor interaction is dominant, is surprisingly triplet and its wave function has directional nodes. A pairing phase diagram for holes in triangular lattices is also presented. \textcopyright{} 1996 The American Physical Society.
We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2{U}^{2}U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.
The two-dimensional (2D) Hubbard model is solved in a new way. The zero-frequency components of the Hubbard interaction are separated out and solved to infinite order to avoid the traditional difficulties associated with perturbation theory in the strong-coupling limit. Specifically the zero-frequency spin interaction is decoupled by the introduction of Stratonovich-Hubbard fields, while the zero-frequency charge interaction is treated by "slave" Hartree-Fock. This approach leads to the formation of large fluctuating spin moments, and as a consequence the one-electron spectral density exhibits a pseudogap. A Metropolis Monte Carlo method is used to perform the configuration averaging over Stratonovich-Hubbard fields. Within single Monte Carlo configurations the non-zero frequency components of the Hubbard interaction are treated by a high-order perturbation method, which incorporates the exchange of dynamical particle-hole fluctuations. Since a single configuration has neither translational symmetry nor spin rotational symmetry, these fluctuations do not have a well-defined crystal momentum or total spin. When the dynamical particle-hole fluctuations are included in the calculation, localized electron pairing results at elevated temperatures. Superconductivity presumably onsets when these localized pairs develop coherence, but this is not studied in the present work. The nature of the pairing interaction and the resulting pair eigenfunctions is studied.