Quantum phase diagram and non-abelian Moore-Read state in double twisted bilayer graphene

TL;DR

This study uses large-scale simulations to identify a non-Abelian Moore-Read topological state in double twisted bilayer graphene, expanding understanding of exotic quantum phases in moiré systems.

Contribution

It demonstrates the presence of a non-Abelian Moore-Read state in double twisted bilayer graphene through comprehensive numerical analysis, a novel finding in this material system.

Findings

Ground state exhibits six-fold near degeneracy.

Finite spectral gap indicates a stable topological phase.

Particle entanglement spectrum confirms Moore-Read state.

Abstract

Experimental realizations of Abelian fractional Chern insulators (FCIs) have demonstrated the potentials of moir\'e systems in synthesizing exotic quantum phases. Remarkably, twisted multilayer graphene system may also host non-Abelian states competing with charge density wave under Coulomb interaction. Here, through larger scale exact diagonalization simulations, we map out the quantum phase diagram for $\nu=1/2$ system with electrons occupying the lowest moir\`e band of the double twisted bilayer graphene. By increasing the system size, we find the ground state has six-fold near degeneracy and with a finite spectral gap separating the ground states from excited states across a broad range of parameters. Further computation of many-body Chern number establish the topological order of the state, and we rule out possibility of charge density wave orders based on featureless density structure factor. Furthermore, we inspect the particle-cut entanglement spectrum to identify the topological state as a non-Abelian Moore-Read state. Combining all the above evidences we conclude that Moore-Read ground state dominates the quantum phase diagram for the double twisted bilayer graphene system for a broad range of coupling strength with realistic Coulomb interaction.