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Acta Physica Polonica A

Bound States of Fermions on 2d Lattice in a Dilute Limit

M. Bąk, R. Micnas

Published Jan 1, 2000• 4 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.97.209

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Journal of Physics Condensed Matter•Oct 3, 2002•28 citations
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 Hubbard model for the square planar lattice in the limit t/U<<1 is discussed. The ground state is chosen to be the product of the Hubbard model's exact solutions for four-site blocks. One-particle excitations appear to be Fermi particles with spin 1 / 2 . Their effective mass near the bottom of the band coincides with the effective mass of excitations in the paramagnetic state in the 'Hubbard-I' approximation. However, minima of the spectrum are situated at other points in the Brillouin zone. The possibility of the binding of two excitations into singlet pair with charge 2e is demonstrated. Cohesive energy is calculated to be equal to 0.1t. The superfluid state of the Bose gas of such pairs is assumed to be connected with high-T c superconductivity.
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)
Abstract Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping t ′ , less mobile carriers produce a stronger fall in v c . For half-filling and t ′ = 0 , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.
We study the superfluid properties of short-coherence-length superconductors described by the extended Hubbard model with on-site repulsive and intersite attractive interaction. We have analysed the superfluid stiffness and thermodynamic properties of the model versus electron concentration and pairing interaction on a two-dimensional square lattice with nearest- and next-nearest-neighbour hopping. The effects of phase fluctuations on anisotropic superconductivity of extended s-and d x 2 − y 2 -wave type were examined within the Kosterlitz–Thouless (KT) scenario. The KT critical temperatures were determined and compared with those from the BCS–Hartree–Fock approximation. The Uemura-type plots, i.e. the critical temperature versus zero-temperature phase stiffness, were obtained for both extended s- and d-wave pairings. The states with mixed (s ∗ and d x 2 − y 2 ) symmetry, and in particular the time-reversal breaking state of s + id symmetry, were analysed and the phase diagrams taking into account these states are presented. We also briefly discuss the crossover from BCS to local pair superconductivity for the d x 2 − y 2 -wave pairing. A comparison of the theoretical results with the experimental data, in particular those of T c versus λ −2 (0), for high- T c cuprate superconductors is made.