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arXiv · 2106.08542

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

Yu-Bo Liu·Yongyou Zhang·Wei-Qiang Chen·Fan Yang
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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.

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Yu-Bo Liu, Yongyou Zhang, Wei-Qiang Chen, Fan Yang. 2021-06-16. $g+ig$ topological superconductivity in the 30$^o$-twisted bilayer graphene. https://arxiv.org/abs/2106.08542

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