Space-Group Approach to the Wavefunction of a Cooper Pair: Nodal Structure and Additional Quantum Numbers for Sr2RuO4 and UPt3
DOI:
https://doi.org/10.15379/2408-977X.2016.05Keywords:
Group theory, Induced representations, Mackey theorem, Unconventional superconductors, Nodal superconductors, Triplet superconductors, Sr2RuO4, UPt3.Abstract
Induced representation method and Mackey theorem on symmetrized squares were applied to construct zero-total-momentum two-electron states in solids, corresponding to Cooper pairs in unconventional superconductors. In this approach the structure of two-electron states depends on the position of one-electron wave vector in a single-electron Brillouin zone. It is shown, that the decomposition of total two-electron basis set results in repeating multidimensional irreducible representations. It is obtained, that in order to label repeating irreducible representation two additional quantum numbers are required: irreducible representation of wave vector group for symmetry planes and directions and quantum numbers on an intermediate group for a general point in a Brillouin zone. Theoretical results are applied to unconventional superconductors UPt3 and Sr2RuO4.
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