Space-group approach to the Ginzburg–Landau phase winding in topological superconductors: application to Sr₂RuO₄

SOP (superconducting order parameter) in topological superconductors is characterized by an IR (irreducible representation) of a point group and a phase winding. In the Ginzburg-Landau theory and in phenomenological symmetry approaches wavefunction of a Cooper pair is identified as a SOP, which is expressed in terms of Legendre polynomials in<i>k</i>-space. In the space-group approach a Cooper pair wavefunction is constructed on the basis of exact one-electron functions in<i>k</i>-space. In the present work a connection between an IR of individual pair and possible phase winding in a pair condensate is investigated group-theoretically. It has been shown that the nodal structure of SOP forD4hsymmetry is defined group-theoretically for one-dimensional IRs and for two-dimensional IRs in the basal plane. For two-dimensional IRs nodes in vertical planes are defined by the additional quantum numbers, i.e. the intermediate group and the labels of its IRs. Experimental nodal structure of SOP in Sr₂RuO₄with nodal basal plane and nodes and dips in vertical planes corresponds to IR<i>E</i>_<i>g</i>. It has been shown using group theory, that when the Ginzburg-Landau theory is extended on two-dimensional IRs of point groups each one of the basis functions has a half of phase winding±πmand total phase winding may be equal to zero or to2πm. Phase winding2πmcorresponds to the magnetic group4/mm'm'. Our results explain a possibility of half quantized flux in Sr₂RuO₄in the presence of external magnetic field and may be used for description of recently obtained phase winding0.3×2πin Ba1-xK_<i>x</i>Fe₂As₂.