Space-group approach to the Ginzburg–Landau phase winding in topological superconductors: application to Sr 2 RuO 4

Source abstract

Abstract 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 k -space. In the space-group approach a Cooper pair wavefunction is constructed on the basis of exact one-electron functions in k -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 for D 4 h symmetry 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 Sr 2 RuO 4 with nodal basal plane and nodes and dips in vertical planes corresponds to IR E g . 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 ± π m and total phase winding may be equal to zero or to 2 π m . Phase winding 2 π m corresponds to the magnetic group 4 / m m ′ m ′ . Our results explain a possibility of half quantized flux in Sr 2 RuO 4 in the presence of external magnetic field and may be used for description of recently obtained phase winding 0.3 × 2 π in Ba 1 − x K x Fe 2 As 2 .