Theoretical Investigation of Fermion Pairing in Three-band Extended Hubbard Model (original) (raw)

Theory of pairing in the Cu-O plane: Three-band Hubbard model and beyond

1999

We calculate the effective interaction W ef f between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a perturbative canonical transformation, to generate a two-body Hamiltonian. Then, we extend the results to all orders. The approach is exact in principle, and we obtain a close analytic expression including explicitly the effects of all virtual transitions to 4-body intermediate states. Our scheme naturally lends itself to embody off-site, inter-planar, phonon-mediated and other interactions which are not considered in the Hubbard model but may well be important. The result depends qualitatively on the symmetry of the two-hole state: 1 B2 and

Pairing in the Three-Band Hubbard Model of the Cu-O Plane

By a canonical transformation of the three-band Hubbard model, we introduce an effective Hamiltonian for the propagation of two holes doped into the ground state of the Cu-O plane. When the pair belongs to the 1 B2 or 1 A2 Irreducible Representations of the C4v Group, the bare holes do not interact by the on-site repulsion; the effective interaction between the dressed holes is obtained analytically in terms of renormalized matrix elements, and generalizes earlier findings from cluster calculations. The Fermi liquid is unstable and numerical estimates with reasonable parameters of the binding energy of the pair are in the range of tens of meV. Our scheme naturally lends itself to embody phonon-mediated and other interactions which cannot occur in the Hubbard model but may give important contributions.

Configuration-interaction approach to hole pairing in the two-dimensional Hubbard model

The interactions between holes in the Hubbard model, in the low density, intermediate to strong coupling limit, are investigated by systematically improving mean field calculations. The Configuration Interaction basis set is constructed by applying to local Unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far appart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for 4 × 4 clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of √ 2 times the lattice spacing, in agreement with exact results and the t-J model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons. PACS number(s): 74.20.-z, 02.70.Lq, 71.10.Fd

Pairing Correlations in the two-layer attractive Hubbard Model

2012

Studies of systems with two fermionic bands with repulsive interaction strength U have a long history, with the Periodic Anderson Model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use Quantum Monte Carlo to study analogous issues for attractive interactions. As in the Periodic Anderson Model, we focus on a case where one band is uncorrelated (U = 0), and focus on the effect of hybridization V between the bands on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are able to explore the physics of doped multi-band attractive systems at low temperatures whereas ground state properties of repulsive models can be determined only at half-filling. For small V , pairing in the U < 0 layer induces pairing in the U = 0 layer. At larger V the ground state of the coupled system loses its superconducting character. The Quantum Monte Carlo data are complemented by results obtained with the Bogoliubov-de Gennes approximation.

Hole pairs in the two-dimensional Hubbard model

The interactions between holes in the Hubbard model, in the low density, intermediate to strong coupling limit, are investigated. Dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. Our results are derived by systematically improving mean field calculations. The method can also be used to derive known properties of isolated spin polarons. PACS number(s): 74.20.-z, 02.70.Lq, 71.10.Fd

Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons

Physical Review B, 1996

A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral t over on-site interaction U , but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in t/U. For the energy the expansion is found to have an accuracy of better than 1% for U/t ≥ 8. A comparison is given with an earlier perturbation expansion based on the Linear Spin Wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed.

Interband pairing in extended two- and three-band Hubbard model

We study the existence of intraband and interband pairing in the extended two band and three-band Hubbard model. It is shown that including interband pairing significantly increases the superconducting critical temperature in comparison with critical temperature of the intraband pairing. This increase allows for decrease of the nearest-neighbor interaction constant necessary for critical temperature in high temperature superconductors to the realistic values.

First-Order Pairing Transition and SingleParticle Spectral Function in the Attractive Hubbard Model

Physical Review Letters, 2002

A Dynamical Mean Field Theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half-filling between a Fermi liquid, stable for U < Uc, and an insulating bound pairs phase for U > Uc, and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low energy structure around the Fermi level, which disappears discontinuously at U = Uc, and two high energy features (Hubbard bands), which persist in the insulating phase. 71.10.Fd, The experimental finding that the (zero-temperature) coherence length of cuprate superconductors is much smaller than for conventional superconductors has suggested that these compounds lie in an intermediate coupling regime, between the weak-coupling and the strongcoupling limits . Moreover, the recent finding from angular resolved photoemission of the existence of a (pseudo) gap in the single-particle spectrum well above the superconducting critical temperature, i.e., in the normal phase, has been usually interpreted in terms of preformed Cooper pairs with no phase coherence. This gave emphasis to the relevant theoretical issues related to the description of the superconducting phase in the crossover regime between the standard BCS and the Bose-Einstein (BE) condensation together with the description of the normal state, where preformed pairs or dynamical superconducting fluctuations give rise to the pseudogap phenomenology. Regarding the pseudogap regime, various perturbative schemes have been adopted, without a firm unambiguous understanding of the electron pairing in the normal state .

Fermion-pairing on a square lattice in extreme magnetic fields

Physica C: Superconductivity, 2002

We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to "k-space", or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C4ν of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down.

Physical pictures of the pairing interaction in the Hubbard model

Journal of Superconductivity, 1994

Physical pictures which have been suggested to describe the pairing interaction in a twodimensional Hubbard model doped near half-filling are compared with numerical Monte Carlo results. We find that the single spin-fluctuation exchange picture provides a reasonable representation if Monte Carlo results are used for the spin susceptibility. We also find that the spatial structure of the pairing interaction in the singlet channel is repulsive when both fermions are on the same site but attractive when they are on near-neighbor sites favouring d; y~ pairing correlations.