Exciton fractional Chern insulators in moiré heterostructures

Abstract

Moiré materials have emerged as a powerful platform for exploring exotic quantum phases. While recent experiments have unveiled fractional Chern insulators exhibiting the fractional quantum anomalous Hall effect based on electrons or holes, the exploration of analogous many-body states with bosonic constituents remains largely uncharted. In this work, we predict the emergence of bosonic fractional Chern insulators arising from long-lived excitons in a moiré superlattice formed by twisted bilayer WSe$_2$ stacked on monolayer MoSe$_2$. Performing exact diagonalization on the exciton flat Chern band present in this structure, we provide compelling evidence for the existence of Abelian and non-Abelian phases at band filling $\frac{1}{2}$ and $1$, respectively, through multiple robust signatures including ground-state degeneracy, spectral flow, many-body Chern number, and particle-cut entanglement spectrum. The obtained energy gap of $\sim 10$ meV for the Abelian states suggests a remarkably high stability of this phase, which persists for a relatively wide range of twist angles and vertical electric fields. Our findings establish the presence of robust bosonic fractional Chern insulators in highly tunable and experimentally accessible moiré heterostructures and unveil a promising pathway for realizing non-Abelian anyons.

Figures (4)

• Figure 1: Nearly ideal exciton Chern band. (a) Schematic illustration of the considered tWSe$_2$--MoSe$_2$ structure. The interlayer excitons X$_1$ and X$_2$ are formed by an electron in MoSe$_2$ and a hole in either of the two WSe$_2$ layers. (b) Exciton band structure for $\Delta=-3.8$ meV and $\theta=1.95^{\circ}$, where the lowest band has a Chern number $C=1$. The color represents the contribution from each exciton species to the band. (c) Berry curvature $\Omega_\mathbf{k} A_\text{BZ}/2\pi$ and (d) Fubini-Study metric $\text{tr}[g_\mathbf{k}] A_\text{BZ}/2\pi$ of the flat band across the moiré Brillouin zone. $A_\text{BZ}$ is the Brillouin zone area.
• Figure 2: Laughlin states at half filling. (a) Many-body energy spectrum containing the 10 lowest energies for each momentum sector, (b) spectral flow, (c) particle-cut entanglement spectrum, and (d) many-body Berry curvature for the two ground states considering contact interactions without kinetic energy effects at $\nu=\frac{1}{2}$. The respective data considering the realistic long-range interaction and the kinetic energy is shown in (e)-(h). The ground states in (a) and (e) are marked in red and have an average many-body Chern number $C_\text{avg}=1/2$. In the PES, the number of states below the first entanglement gap (denoted by the red solid line) is $1287$, matching the number of quasi-hole excitations in the $\nu=\frac{1}{2}$ Laughlin states. The considered system has $N_\text{s}=18$ moiré sites.
• Figure 3: Stability of Laughlin states in the $(\theta,\Delta)$ parameter space, where $\theta$ is the twist angle and $\Delta$ is the energy offset between the two interlayer exciton resonances. (a) Energy gap in the many-body spectrum between the Laughlin ground states and excited states at filling $\nu=\frac{1}{2}$ in a system of $N_\text{s}=12$ sites with long-range interaction. (b) Bandwidth of the lowest single-particle exciton band.
• Figure 4: Moore--Read states at filling one. Many-body spectrum (10 lowest energies) and PES at $\nu=1$ with long-range interactions for (a)-(b) 13 and (c)-(d) 14 particles. The single and threefold quasi-degenerate ground states (red dots in panels (a) and (c)) for an odd and even particle number of sites are located at the momenta expected for MR states. The red line in panels (b) and (d) indicates the entanglement gap respecting the quasi-hole counting rules of the MR state (416 and 518 quasihole excitations for 13 and 14 particles with $N_A=3$).