High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

TL;DR

This paper explores the emergence of high-angular-momentum topological superconductivity in large-angle twisted homo-bilayer systems with quasi-crystal structures, proposing a universal theory and analyzing specific material examples.

Contribution

It introduces a universal Ginzburg-Landau framework and microscopic models to predict HAM topological superconductivity in LA-THB systems, including specific material cases.

Findings

HAM TSCs with angular momentum L=4,5,2 can emerge in twisted bilayer systems.

Interlayer Josephson coupling induces specific pairing angular momenta based on symmetry.

Theoretical framework applies to graphene, BC3, and cuprate bilayers.

Abstract

We study the largest-angle twisted homo-bilayer (LA-THB) systems, hosting Moir\'eless quasi-crystal (QC) structure. We propose to use these materials to generate high-angular-momentum (HAM) topological superconductivities (TSCs) protected by their QC symmetries absent on conventional crystalline materials. This proposal is based on our universal Ginzburg-Landau theory based analysis which yields the general conclusion that, when each $D_n$-symmetric ($n$ is even) monolayer hosts SC with pairing angular momentum $l\le \frac{n}{2}$, the interlayer Josephson coupling will induce SC with pairing angular momentum $L=l$ or $L=n-l$ in the LA-THB, determined by microscopic details. The latter one is just the HAM TSC if $l>0$. Based on our revised perturbational-band theory, we develop general microscopic framework to study the QC LA-THBs involving electron-electron interactions, adopting which we study three examples, i.e. the 30$^\circ$- twisted bilayer graphene, the 30$^\circ$- twisted bilayer BC$_3$, and the 45$^\circ$- twisted bilayer cuprates. The $g+ig$- $h+ih$- and $d+id$- TSCs with HAM $L=4,5$ and $2$ can emerge in certain doping regimes in these systems, respectively.