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Acta Physica Polonica A

Resonant Two-Electron Pairs in a Simple Cubic Lattice

M. Bąk

Published Oct 1, 2014• 0 citations
Publisher

Abstract

The properties of resonant two-electron pairs are examined in three-dimensional simple cubic extended Hubbard tUW model, in sand dsymmetry channels, in the limit of empty lattice.Lattice Green function technique is applied to calculate the scattering amplitude by means of T matrix for any energy in the band on Γ R line within the Brillouin zone.The analysis shows the persistence of resonant states even for Coulomb interactions so weak that the equation for the resonant states is not formally fullled.The dierence in behavior of resonances controlled by on-site and intersite Coulomb interactions is found.The ranges of applicability of approximate formula for the actual position of resonant peak and its width are shown.

DOI
10.12693/aphyspola.126.a-63

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The properties of resonant two-electron pairs are examined in three-dimensional simple cubic extended Hubbard tUW model, in sand dsymmetry channels, in the limit of empty lattice.Lattice Green function technique is applied to calculate the scattering amplitude by means of T matrix for any energy in the band on Γ R line within the Brillouin zone.The analysis shows the persistence of resonant states even for Coulomb interactions so weak that the equation for the resonant states is not formally fullled.The dierence in behavior of resonances controlled by on-site and intersite Coulomb interactions is found.The ranges of applicability of approximate formula for the actual position of resonant peak and its width are shown.
Resonant two-electron states are examined in attractive Hubbard model on simple cubic lattice and exact formula for scattering cross section in the limit of low density (empty lattice) is calculated.S-wave pair is considered by means of lattice Green functions (LGF).Analytical form of these functions found by Joyce is used facilitating calculations, which were greatly hindered before by the necessity of using LGF's tabulated values.It is found that the actual peak of scattering cross-section is formed on the lower band boundary in discrepancy with formulae of the theory of scattering in solids.
The physical property of strongly correlated electrons on a three-dimensional (3D) 3 x 3 x 3 cluster of the simple cubic lattice is here presented.In the work we developed the unit step Hamiltonian as a solution to the single band Hubbard Hamiltonian for the case of two electrons interaction in a finite three dimensional lattice.The approximation to the Hubbard Hamiltonian study is actually necessary because of the strong limitation and difficulty pose by the Hubbard Hamiltonian as we move away from finite -size lattices to larger N -dimensional lattices.Thus this work has provided a means of overcoming the finite -size lattice defects as we pass on to a higher dimension.We have shown in this study, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.This study reveals that when the Coulomb interaction is zero, that is, for free electron system (non-interacting), thevariational parameters which describe the probability distribution of lattice electron system is the same.The spectra intensity for on-site electrons is zero for all values of the interaction strength.
We study the one-band Hubbard model in a three dimensional simple cubic lattice, with periodic boundary conditions, by means of a variational analytic approach. Ground state energies and pairing correlations depend implicitly on the interaction strength (U/41). It is shown that for two electrons, the interaction is always repulsive in the ground state for any positive value of the on-site Coulomb interaction U. Implications of this result for superconductivity are also discussed. Nigerian Journal of Physics Vol. 16(2) 2004: 167-171
We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.
Abstract The properties of the bound states on a lattice is an interesting problem related to the properties of superconductivity and Bose–Einstein condensation in a given model. By means of the exact solution of the Schrödinger equation the properties of the bound pairs on a frustrated, triangular lattice are examined within extended Hubbard model. Dispersion curves and mobilities are calculated for both positive and negative sign of the hopping integral. The possibility of increasing the mobility with increasing intersite Coulomb interaction is found. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)