Abstract: 2023 welcomed a new member to the small family of experimentally realized, topologically ordered phases of matter: fractional quantum anomalous Hall fluids. Observed in MoTe2 and hBN-multilayer graphene moiré superlattices to date [1,2], these states provide fertile grounds for novel interplay between topological order and broken symmetry.

I will discuss insights and predictions regarding the quantum phase diagram of twisted MoTe2 emerging from finite-size numerical diagonalization studies. First, we show that the moiré miniband model of Wu et. al. [3] for this system leads to ferromagnetism and FQAH states at the observed filling fractions robustly with respect to model parameters [4]. Second, our studies reveal strong particle-hole asymmetry and show that charge density wave states and spin/valley polarized metals outcompete quantum-Hall-like phase at filling factors near n=0 and n=1 holes per moiré unit cell respectively [5]. Third, we predict an “anomalous composite Fermi liquid”, a compressible fluid with zero Drude weight and Hall conductance approaching e2/(2h) in the clean limit, near n=1/2 [6]. Finally, I will discuss the prospect of non-Abelian FQAH states at half filling of the second miniband [7]. Wavefunction overlap analysis indicates that these states are likely to realize the topological order of the Moore-Read Pfaffian state in the thermodynamic limit.

Refs:

• [1] Cai, Jiaqi, et al. Nature 622.7981 (2023): 63-68.; Zeng, Yihang, et al. Nature 622.7981 (2023): 69-73.; Park, Heonjoon, et al. Nature 622.7981 (2023): 74-79.; Xu, Fan, et al. Physical Review X 13.3 (2023): 031037.
• [2] Lu, Zhengguang, et al. Nature 626.8000 (2024): 759-764.
• [3] Wu, Fengcheng, et al. Physical review letters 122.8 (2019): 086402.
• [4] Reddy, Aidan P., et al. Physical Review B 108.8 (2023): 085117.
• [5] Reddy, Aidan P., and Liang Fu. Physical Review B 108.24 (2023): 245159.
• [6] Goldman, Hart, et al. Physical Review Letters 131.13 (2023): 136501.
• [7] Reddy, Aidan P., et al. arXiv preprint arXiv:2403.00059(2024).