Additional quantum numbers for two-electron states in solids. Application to topological superconductor UPt3

Abstract

Abstract Topological superconductors, which are assumed to be a key ingredient for topological quantum computing, reveal unconventional structures of their superconducting order parameter (SOP), which is usually represented by model functions. However, the central problem of the theory of topological superconductivity is to describe the observed topological structures of SOP in terms of quantum mechanics and group theory. In present work making use of the Anderson ansatz for a Cooper pair and induced representation method a complete group theoretical classification of chiral states in D 6h symmetry (point symmetry group of topological superconductor UPt3) is performed. In this technique topological invariant phase winding is defined by the complex irreducible representation (IR) of symmetry group D 6h , whose structure strongly depends on additional quantum numbers, which are the labels of IRs of Cooper pair’s rotational symmetry group C 6h . The technique is extended on the description of time reversal symmetry of the state in terms of Shubikov groups, and B phase of UPt3 with horizontal nodal plane only was connected with corepresentation Δ + E ′ 2 u of magnetic group 6/mm′m′. The structure of A phase with vertical nodes 45° to a axis is a combinations of two complex conjugate E 2u states. Twofold spontaneous symmetry breaking in C phase is connected with the E 1u SOP.