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physica status solidi (b)

Bound electron pairs on a triangular lattice in an extended Hubbard model

M. Bąk

Published Apr 12, 2007• 11 citations
Publisher

Abstract

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)

DOI
10.1002/pssb.200674603

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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)
We examine extended bound states in a dilute limit of the extended Hubbard model on the two-dimensional square lattice.By solving exactly the two-body problem we have determined the binding energies, mobilities, and dispersion curves across the Brillouin zone for bound states of various symmetries.It turns out that the d-wave pairing is strongly favored by the nnn hopping and the intersite local pairs can have small effective masses, even in the case of strong binding.We have also found a possibility of extended S-d2-2 mixing of the bound states.
We examine extended bound states in the dilute limit of the extended Hubbard model with next-nearest-neighbour (nnn) hopping and nnn interactions on the two dimensional square lattice. By the exact solution of a two-body problem we show that d-wave pairing is strongly favored by the nnn hopping. We determine the binding energies, mobilities and dispersion curves across Brillouin zone (B.z.) for bound states of various symmetries. The numerical analysis shows that the deep bound states can exist in the whole B.z. and we have also found s*-d mixing of the bound states.
The properties of a dilute electron gas, coupled to the lattice degrees of freedom, are studied and compared with the properties of an electron gas at half-filling, where spinless fermions with two orbitals per lattice site are considered. The simplest model which includes both the local electron-lattice interaction of the Jahn-Teller type and the electronic correlations is the E ⊗ β-Jahn-Teller-Hubbard model. We analyze the formation and stability of Jahn-Teller polarons and bipolarons, respectively. Our approach is based on a hopping expansion in the strong-coupling regime. The results are compared with recently published findings for the Hubbard-Holstein model [1, 2]. The special case of the Jahn-Teller-Hubbard model at half-filling is mapped on a spin-1/2 Heisenberg model with phonon-dependent coupling constants. This has been derived within a projection formalism that provides a continued-fraction representation of the Green's function. We study the exact solution for two and three particles and compare it with the effective theory on the infinite lattice with one particle per site. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract We analyze the competing pairings and crossover from BCS to local pair (LP) superconductivity for the d ‐wave pairing symmetry in the ground state. The phase diagrams for the extended Hubbard model with intersite electron pairing and hard‐core repulsion (U = ∞) are obtained for the 2D square lattice. The influence of the nnn hopping (t 2) on the crossover is discussed. For appropriate values of the parameters (nnn repulsion) and |t 2/t | < 0.5 the crossover is simultaneous with the vanishing of nodal points in the quasiparticle energy. The vanishing of nodal points is clearly reflected in the evolution of the presented superconducting characteristics. Results for d pairing are compared with those for the crossover in the s*‐wave channel and the role of chiral px + i py states is also discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)