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AIP conference proceedings

Triplet Vortex Lattice Solutions of the Bogoliubov-de Gennes Equation in a Square Lattice

Yoshiki Hori, Akira Goto, Masa-aki Ozaki

Published Jan 1, 2006• 0 citations
Publisher
DOI
10.1063/1.2354966

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We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov--de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.