Phase fluctuations of s-wave superconductors on a lattice

TL;DR

This paper derives an extended XY model for phase fluctuations in s-wave superconductors on a lattice, revealing a larger fluctuation region between the superconducting transition and the pseudogap temperature.

Contribution

It introduces an effective Hamiltonian incorporating higher neighbor interactions, extending the traditional XY model to better describe phase fluctuations in lattice superconductors.

Findings

Effective Hamiltonian of extended XY type derived

Larger fluctuation region between T_c and pseudogap temperature identified

Model reduces to simple XY in the continuum limit

Abstract

Based on an attractive $U$ Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we finally arrive at is of the extended XY type. While it correctly reduces to a simple XY in the continuum limit, in the general case, it contains higher neighbor interaction in spin space. An important feature of our Hamiltonian is that it gives a much larger fluctuation region between the Berezinskii-Kosterlitz-Thouless transition temperature identified with $T_{c}$ for superconducting and the mean field transition temperature identified with the pseudogap temperature.