Acta Physica Polonica A

Properties of the Bound States on a Hexagonal Lattice

M. Bąk

Published May 1, 2007• 1 citation

Abstract

Two electrons on a lattice pose an interesting problem which can be solved exactly.When the effective interactions are strong enough, the bound states are formed.The properties of such bound pairs in an extended Hubbard model are examined for both signs of nearest neighbor hopping integral t.The stabilization of s * -wave pairing is found for t < 0 and of f -wave for t > 0. Phase diagrams for the existence of none, one or two s * -wave solutions are calculated.

DOI: 10.12693/aphyspola.111.781

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Acta Physica Polonica A

Properties of the Bound States on a Hexagonal Lattice

M. Bąk

Published May 1, 2007• 1 citation

Publisher

Abstract

DOI: 10.12693/aphyspola.111.781

Related papers

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Pairing operators of electrons with an arbitrary distance on a square lattice are defined in each possible wave channel, s, p,

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

{\mathit{d}}_{\mathit{x}\mathit{y}}

, and

{\mathit{g}}_{\mathit{x}}^{3}

{\mathit{xy}}^{3}

. Exact identities among pairing amplitudes in the Hubbard model are presented, giving powerful constraints on the nature of pairings. At half filling, some of the pairing amplitudes, including those of the second-shortest pairing distance, vanish identically in each wave channel except the p wave. There are correlations among pairing amplitudes away from half filling, as well as nonidentically vanishing ones at half filling. Even if the pairing amplitudes vanish up to a certain distance, those of larger distances can still possibly be nonzero. The order of magnitude is estimated for the pairine amplitudes, indicating that those of large distances can by no means be neglected. The scheme is also used in the extended Hubbard model including nearest-neighbor density-density interaction and that including next-nearest-neighbor hopping. In that including nearest-neighbor interaction, the features of pairing amplitudes are just the same as in the original Hubbard model at half filling, and are also similar away from half filling, but with the difference that the amplitude is now dependent on the nearest-neighbor interaction. In the model including next-nearest-neighbor hopping, the features are quite different, the constraint identities are more underconstrained, and the amplitude has no monotonic dependence upon the pairing distance if the next-nearest-neighbor hopping has an opposite sign to the nearest-neighbor hopping as required physically. The same scheme is also used to discuss the possible pairings in the coupled two-plane Hubbard model and in the infinite-layer Hubbard model.