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 MoTe
2 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 e
2/2h 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.
[1] Cai, Jiaqi, et al. Nature (2023); Zeng, Yihang, et al. Nature (2023); Park, Heonjoon, et al. Nature (2023); Xu, Fan, et al. Physical Review X (2023).
[2] Lu, Zhengguang, et al. Nature (2024)
[3] Wu, Fengcheng, et al. Physical review letters (2019)
[4] Reddy, Aidan P., et al. Physical Review B (2023)
[5] Reddy, Aidan P., and Liang Fu. Physical Review B (2023)
[6] Goldman, Hart, et al. Physical Review Letters (2023)
[7] Reddy, Aidan P., et al. "Non-Abelian fractionalization in topological minibands." Physical Review Letters (2024)
