A pure Hubbard model with demonstrable pairing adjacent to the Mott-insulating phase

TL;DR

This paper introduces a Hubbard model on frustrated geometries, demonstrating that holes tend to form bound pairs in low-spin states, which is relevant to understanding pairing mechanisms in high-temperature superconductors.

Contribution

The study provides an exact solution showing hole pairing in a frustrated Hubbard model, highlighting a potential mechanism for pairing in high-temperature superconductors.

Findings

Holes form bound pairs with increasing size as binding energy decreases.

Ground state transitions from ferromagnetic to low-spin depending on intra-pair hopping.

Hole motion alone can generate short-range pairing in frustrated geometries.

Abstract

We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intra-pair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1-d and 2-d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole motion in the copper-oxide planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone.