Octupolar Weyl Superconductivity from Electron-electron Interaction

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 $d_{3z^2-r^2}+i{d}_{x^2-y^2}$-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 $p_x+i{p}_y$ (e.g ${}^3$He-A) and $d_{x^2-y^2}+i{d}_{xy}$ 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.

arXiv comment7+9 pages, 3+3 figures