Robust Non-abelian fractional Chern insulators in twisted multilayer graphene

Experimental realizations of Abelian fractional Chern insulators (FCIs) have demonstrated the potentials of moiré systems in synthesizing exotic quantum phases. Recently, a twisted multi-layer graphene model have been proposed to engineer topological flat bands mimicking higher landau levels and a subsequent numerical study found possible Moore-Read states and charge density wave states in the band model under Coulomb interaction. Here, through large scale exact diagonalization method, we perform comprehensive analysis on the robustness of Moore-Read states in this model. By increasing the system size, we find the spectral gap remains finite for a broad range of parameters. Further computation of many-body Chern number and the structure factor rule out possibility of charge density wave orders. Finally, we inspect the particle cut entanglement spectrum. Combining all the above evidences we conclude that robust Moore-Read ground states exist in the twisted multilayer graphene model.