Triplet superconductivity in quasi one-dimensional systems

TL;DR

This paper investigates the conditions under which triplet superconductivity arises in a one-dimensional Hubbard model with various interactions, combining analytical and numerical methods to map the phase diagram.

Contribution

It provides a simple necessary condition for triplet superconductivity in the model and compares weak-coupling predictions with exact numerical results.

Findings

Triplet correlations dominate when 4V+J<0.

Correlated hopping requires negative three-body interaction for positive V.

Numerical results confirm the phase diagram predictions.

Abstract

We study a Hubbard hamiltonian, including a quite general nearest-neighbor interaction, parametrized by repulsion V, exchange interactions Jz, Jperp, bond-charge interaction X and hopping of pairs W. The case of correlated hopping, in which the hopping between nearest neighbors depends upon the occupation of the two sites involved, is also described by the model for sufficiently weak interactions. We study the model in one dimension with usual continuum-limit field theory techniques, and determine the phase diagram. For arbitrary filling, we find a very simple necessary condition for the existence of dominant triplet superconducting correlations at large distance in the spin SU(2) symmetric case: 4V+J<0. In the correlated hopping model, the three-body interaction should be negative for positive V. We also compare the predictions of this weak-coupling treatment with numerical exact results for the correlated-hopping model obtained by diagonalizing small chains, and using novel techniques to determine the opening of the spin gap.