$g+ig$ topological superconductivity in the 30$^o$-twisted bilayer graphene

TL;DR

This paper predicts a novel $g+ig$ topological superconducting state in 30° twisted bilayer graphene, characterized by unique angular momentum and symmetry properties, arising from interaction-driven pairing in a quasicrystal structure.

Contribution

It introduces the $g+ig$ topological superconductivity in twisted bilayer graphene, highlighting its unique symmetry and origin from Josephson coupling, expanding understanding of quasicrystal superconductivity.

Findings

Prediction of $g+ig$ topological superconductivity in twisted bilayer graphene.

Identification of the pairing symmetry and angular momentum of the $g+ig$ state.

Explanation of the $g+ig$ state originating from Josephson coupling between layers.

Abstract

Based on our revised perturbational-band theory, we study possible pairing states driven by interaction in the electron-doped quasicrystal 30\degree-twisted bilayer graphene. Our mean-field study on the related t-J model predicts that, the beneath-van-Hove and beyond-van-Hove low doping regimes are covered by the chiral $d+id$ and $g+ig$ topological superconductivities (TSCs) respectively. The $g+ig$-TSC possesses a pairing angular momentum 4, and hence following each effective $C_{12}$- rotation by $\Delta\phi=n\pi/6$, the pairing phase changes $4\Delta\phi$. This intriguing TSC is novel, as it belongs to a special 2D $E_4$- irreducible representation of the effective $D_{12}$ point group unique to this quasicystal and absent on periodic lattices. The Ginzburg-Landau theory suggested that the $g+ig$- TSC originates from the Josephson coupling between the $d+id$ pairings on the two mono-layers.