Fractional quantum anomalous Hall and anyon density-wave halo in a minimal interacting lattice model of twisted bilayer MoTe$_2$

Abstract

The experimental discovery of fractional quantum anomalous Hall (FQAH) states in tunable moiré superlattices has sparked intense interest in exploring the interplay between topological order and symmetry breaking phases. In this paper, we present a comprehensive numerical study of this interplay through large-scale density matrix renormalization group (DMRG) simulations on a minimal two-band lattice model of twisted bilayer MoTe$_2$ at filling $ν=-2/3$. We find robust FQAH ground states and provide clear numerical evidences for anyon excitations with fractional charge and pronounced real-space density modulations, directly supporting the recently proposed anyon density-wave halo picture. We also map out the displacement field dependent phase diagram, uncovering a rich landscape of charge ordered states emerging from the FQAH, including a quantum anomalous Hall crystal (QAHC) with an integer quantized Hall conductance. We expect our work to inspire further research interest of intertwined correlated topological phases in moiré systems.

Figures (4)

• Figure 1: (a) Density distribution of the Wannier functions, with Wannier centers indicated by stars and moiré unit cell shown as dashed line. (b) Comparison of the band structure between the tight-binding model and the continuum model. (c) Illustration of the hopping terms in tight-binding model on a honeycomb lattice. The next nearest neighbor hopping $t_2$ carry phase $+2\pi/3$ along the indicated arrow direction.
• Figure 2: (a) Single particle Green's functions for various NN interaction $V_1$. (b) Real space density profile $\langle n_i\rangle$ at $V_1=8$ meV. (c) The same density distribution averaged along $y$ direction. (d) Connected density correlations for different NN interaction $V_1$ in linear (semi-log) scale for main (inset) figure. (e) Adiabatic charge pumping under insertion of $2\pi$ flux thread through the cylinder at $V_1=8$ meV. The upper panel shows the local density change, while the lower panel shows its cumulative sum from the left boundary, where the color shading indicates the magnitudes of the inserted flux.
• Figure 3: (a) $y$-direction averaged real space density profile for the FQAH at $V_1=8$ meV (black) and for the system with one added electron (red). (b) Density difference $\langle \Delta n_i\rangle$ between these two systems. (c) Cumulative sum of the density difference from the left boundary. The gray dashed lines at $0, 1/3, 2/3, 1$ mark the expected fractionally quantized value of charge. (d) Real space density distribution for the added-electron system in (a). (e) Real space distribution for the density difference in (b).
• Figure 4: (a) Ground state phase diagram as a function of NNN interaction $V_2$ and displacement field $D$ at fixed NN interaction $V_1=10$ meV, obtained using $L_x=25$ cylinders. The stripe region is depicted only schematically by an orange shade. (b-d) Real space density distribution $\langle n_i\rangle$ for three representative systems in different charge ordered phases marked by stars in the phase diagram: (b) $V_2=0$ meV, $D=0.5$ meV; (c) $V_2=3$ meV, $D=1$ meV; (d) $V_2=3$ meV, $D=5$ meV. (e) Single particle Green's functions $\langle c_i^\dagger c_j\rangle$ for various displacement fields $D$ at $V_1=10$ meV and $V_2=0$ meV, obtained from $L_x=49$ cylinders. (f, g) Adiabatic charge pumping under insertion of $2\pi$ flux for the same representative systems as in (c) and (d), where the color shading indicates the magnitudes of the inserted flux.