Classification of multipole superconductivity in multi-orbital systems and its implications

TL;DR

This paper classifies unconventional multipole superconductivity in multi-orbital systems with spin-orbit interactions, revealing new gap structures and the potential for electron-phonon driven unconventional superconductivity.

Contribution

It provides a group-theoretical classification of multipole superconductivity in symmorphic space groups, uncovering novel gap features and mechanisms.

Findings

Superconducting gap functions with nontrivial momentum dependence in D6 symmetry.

Unconventional gap structures can arise from local interactions, including electron-phonon coupling.

Line nodes and gap minima are inevitable due to orbital symmetry, explaining anisotropic s-wave superconductivity.

Abstract

Motivated by a growing interest in multi-orbital superconductors with spin-orbit interactions, we perform the group-theoretical classification of various unconventional superconductivity emerging in symmorphic $\rm O$, $\rm D_4$, and $\rm D_6$ 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 been overlooked in the long history of research in this field: (1) A superconducting gap function with $\varGamma_9\otimes\varGamma_9$ in $\rm D_6$ possesses nontrivial momentum dependence, different from the usual spin 1/2 classification. (2) Unconventional gap structure can be realized in the BCS approximation of purely local (on-site) interactions irrespective of attractive/repulsive. 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 without any competitive fluctuations.