W= 0 pairing in Hubbard and related models of low-dimensional superconductors

Abstract

Abstract. Lattice Hamiltonians with on-site interaction W have W = 0 solutions, that is, many-body singlet eigenstates without double occupation. In particular, W = 0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W = 0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO 2 planes of cuprate superconductors, armchair Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W = 0 pairs quantize the magnetic flux like superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W = 0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the 4 × 4 Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W = 0 pairing mechanism both at weak coupling and in the polaronic regime.

Exact thermodynamics of pairing and charge–spin separation crossovers in small Hubbard nanoclusters

“…The fact that electron pairing can arise directly from the on-site electron repulsion between electrons in small clusters was found quite early [33,34,35,36]. However, it is not a priori obvious that such a mechanism in an ensemble of small clusters can survive at finite temperatures.…”

Theoretical approach to electronic screening and correlated superconductivity in carbon nanotubes

“…The findings of Ref.22 are based on the so called W = 0 theory 23 ; this provides a singlet pairing mechanism operating on a lattice with Hubbard interaction and is otherwise somewhat analogue to the Kohn-Luttinger mechanism 24 . On the basis of symmetry arguments, it is possible to show that the Hamiltonian in Eq.…”

“…As a consequence the electrons forming a W = 0 pair have no direct interaction and are good candidates to achieve bound states. Their effective interaction V 22 comes out from virtual electron-hole excitation exchange with the Fermi sea and in principle can be attractive 23 . The binding energy ∆ of the W = 0 pairs for an armchair (n, n) nanotube can be obtained by solving the gap equation…”

Correlated nanoscopic Josephson junctions

“…A typical double-minimum pattern is found with sharp maxima due to the level crossing of paired states with different symmetry. This patter is obtained with t Ox = −0.05; if the absolute value of the hopping t Ox is increased too much, the coupling to the flux becomes excessive compared to the pairing energy and the system turns paramagnetic 5 . There are two minima at φ = φ0…”

“…We focus on repulsive Hubbard-like models that we want to test for correlation-induced superconductivity; this is relevant to the search for possible nonconventional mechanisms that have been considered by several workers, for example in the context of high-T C materials. The choice of the geometry has been prompted by previous studies [4] in the framework of the W = 0 theory; this develops the role of symmetry in inducing pairing from repulsive interactions. We also found the conditions leading to superconducting flux quantization in mesoscopic systems.…”