Quantum anomalous, spin, and valley Hall states in pentalayer rhombohedral graphene moiré superlattices

Since the quantum anomalous Hall effect was observed [1], pentalayer rhombohedral graphene moiré superlattices have been intensively studied. Here, we extend quantum anomalous Hall physics at a moiré filling factor of ν=1 [2] to more complex scenarios at higher filling factors. Specifically, we demonstrate that at ν=2, many-body effects can lead to the emergence of quantum spin Hall and quantum valley Hall states, without the need for spin-orbit coupling or valley-dependent potentials. Moreover, at filling factors ν=3 and ν=4, we numerically show that the ground state consists of both topological and nontopological bands, illustrating a complex interplay that disrupts the straightforward relationship typically observed between ν and 4-ν [3].

[1] Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Nature 626, 759 (2024).

[2] Z. Dong, A. S. Patri, and T. Senthil, arXiv: 2311.03445; B. Zhou, H. Yang, and Y.-H. Zhang, arXiv: 2311.04217; J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath, and D. E. Parker, arXiv: 2311.05568; Z. Guo, X. Lu, B. Xie, and J. Liu, Phys. Rev. B 110, 075109(2024); Y. H. Kwan, J. Yu, J. Herzog-Arbeitman, D. K. Efetov, N. Regnault, and B. A. Bernevig, arXiv: 2312.11617.

[3] K. Kudo, R. Nakai, and K. Nomura, arXiv: 2406.14354.