Moir\'e Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices

Jonah Herzog-Arbeitman; Yuzhi Wang; Jiaxuan Liu; Pok Man Tam; Ziyue Qi; Yujin Jia; Dmitri K. Efetov; Oskar Vafek; Nicolas Regnault; Hongming Weng; Quansheng Wu; B. Andrei Bernevig; Jiabin Yu

arXiv · 2311.12920

Moir\'e Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices

Jonah Herzog-Arbeitman·Yuzhi Wang·Jiaxuan Liu·Pok Man Tam·Ziyue Qi·Yujin Jia·Dmitri K. Efetov·Oskar Vafek·Nicolas Regnault·Hongming Weng·Quansheng Wu·B. Andrei Bernevig·Jiabin Yu

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Abstract

The experimental discovery of fractional Chern insulators (FCIs) in rhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) has preceded theoretical prediction. Supported by large-scale first principles relaxation calculations at the experimental twist angle of $0.77^\circ$, we obtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedral graphene-hBN moir\'e systems. Focusing on the pentalayer case, we analytically explain the robust $|C|=0,5$ Chern numbers seen in the low-energy single-particle bands and their flattening with displacement field, making use of a minimal two-flavor continuum Hamiltonian derived from the full model. We then predict nonzero valley Chern numbers at the $\nu = -4,0$ insulators observed in experiment. Our analysis makes clear the importance of displacement field and the moir\'e potential in producing localized "heavy fermion" charge density in the top valence band, in addition to the nearly free conduction band. Lastly, we study doubly aligned devices as additional platforms for moir\'e FCIs with higher Chern number bands.

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Jonah Herzog-Arbeitman, Yuzhi Wang, Jiaxuan Liu, Pok Man Tam, Ziyue Qi, Yujin Jia, Dmitri K. Efetov, Oskar Vafek, Nicolas Regnault, Hongming Weng, Quansheng Wu, B. Andrei Bernevig, Jiabin Yu. 2023-11-21. Moir\'e Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices. https://arxiv.org/abs/2311.12920

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