Phase Fluctuations of s-Wave Superconductors on a Lattice

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 Tc for superconducting and the mean field transition temperature identified with the pseudogap temperature.