Octupolar Weyl Superconductivity from Electron-electron Interaction

TL;DR

This paper predicts a novel octupolar Weyl superconductivity with unique topological properties arising from electron-electron interactions in cubic symmetry, featuring complex pairing symmetries and Majorana surface states.

Contribution

It introduces a new superconducting pairing symmetry with octupolar orbital angular momentum, leading to 3D Weyl topological superconductivity with Majorana arcs.

Findings

Dominant pairing symmetry is $d_{3z^2-r^2}+id_{x^2-y^2}$-type.

Develops octupolar $O_{xyz}$ orbital angular momentum in Cooper pairs.

Results suggest potential material realizations and experimental tests.

Abstract

Unconventional superconductivity arising from electron-electron interaction can manifest exotic symmetry and topological properties. We investigate the superconducting pairing symmetry problem based on the 3D cubic $O_h$ symmetry with both weak- and strong-coupling approaches. The dominant pairing symmetries belong to the two-dimensional $E_g$ representation at low and intermediate doping levels, and the complex mixing gap function of the $d_{3z^2-r^2}+id_{x^2-y^2}$-type is energetically favored in the ground state. Cooper pairs with such a symmetry do not possess orbital angular momentum (OAM) moments, which is different from other time-reversal symmetry breaking pairings such as $p_x+ip_y$ (e.g $^3$He-A) and $d_{x^2-y^2}+id_{xy}$ under the planar hexagonal symmetry. Instead, they develop the octupolar $O_{xyz}$ component of OAM, which results in 8 nodal points along the body diagonal directions exhibiting an alternating distribution of monopole charges $\pm 1$. This leads to an intriguing 3D Weyl topological SC, which accommodates nontrivial surface states of Majorana arcs. Our results appeal for material realizations and experimental tests in optical lattices.