Abstract
The Bogoliubov–de Gennes equations for singlet superconductivity in an exchange field are analyzed with real materials having complex Fermi surfaces in mind. The resulting gap equation is reformulated in terms of a velocity spectrum on the Fermi surface in which the surface geometry is built in. The resulting analysis can readily be used for arbitrary dispersion relations. Fulde-Ferrell-Larkin-Ovchinnikov FFLO phases are studied in the temperature-field plane, with results providing a physically clear interpretation of why certain directions of pair momentum q are energetically favored. We present clarifying results for models the two-dimensional square Fermi surface, one-, two-, and three-dimensional isotropic surfaces and provide an application to the weak ferromagnetic ZrZn2 showing it is not a favorable case for an FFLO phase.
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