Classification of “multipole” superconductivity in multiorbital systems and its implications

Abstract

Motivated by a growing interest in multiorbital superconductors with spin-orbit interactions, we perform the group-theoretical classification of various unconventional superconductivity emerging in symmorphic $O, {D}_{4}$, and ${D}_{6}$ space groups. The generalized Cooper pairs, which we here call ``multipole'' superconductivity, possess spin-orbital coupled (multipole) degrees of freedom, instead of the conventional spin singlet/triplet in single-orbital systems. From the classification, we obtain the following key consequences, which have never been focused in the long history of research in this field: (1) A superconducting gap function with ${\mathrm{\ensuremath{\Gamma}}}_{9}\ensuremath{\bigotimes}{\mathrm{\ensuremath{\Gamma}}}_{9}$ in ${D}_{6}$ possesses nontrivial momentum dependence different from the usual spin-$\frac{1}{2}$ classification. (2) Unconventional gap structure can be realized in the BCS approximation of purely local (onsite) interactions irrespective of attraction/repulsion. It implies the emergence of an electron-phonon (e-ph) driven unconventional superconductivity. (3) Reflecting symmetry of orbital basis functions there appear not symmetry protected but inevitable line nodes/gap minima, and thus, anisotropic $s$-wave superconductivity can be naturally explained even in the absence of competing fluctuations.