Fractional Quantum Anomalous Hall State and Anyon Density-Wave Halo Found in MoTe at Filling

The pursuit of exotic quantum states in twisted bilayer materials has revealed a fascinating interplay between topology and symmetry, and recent experiments demonstrate fractional anomalous Hall (FQAH) effects in these systems. Chuyi Tuo, Ming-Rui Li, and Hong Yao, from Tsinghua University, investigate this phenomenon using advanced computational modelling, focusing on a minimal theoretical description of twisted bilayer MoTe. Their work establishes the existence of robust FQAH states and provides compelling evidence for anyon excitations, quasiparticles with fractional charge, arranged in a distinctive density wave pattern. This research significantly advances understanding of correlated topological phases in moiré materials, and unveils a complex phase diagram including novel charge-ordered states, potentially paving the way for new quantum technologies.

This paper presents 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 MoTe2 at filling ν = −2. The team finds robust FQAH ground states and provides clear numerical evidence for anyons.

Wannier Functions and Adiabatic Charge Pumping

The study details the construction of tight-binding models using well-localized Wannier functions, created through a multi-step process of wavefunction polarization, gauge fixing, and projection. These functions form the basis for DMRG simulations and are crucial for accurate modeling of the material’s electronic structure. The method also details how Hall conductance is calculated using adiabatic charge pumping, gradually inserting magnetic flux to induce charge transfer, and verifying the topological properties of the system. Additional real-space density profiles confirm the charge pumping process in the FQAH, quantum anomalous Hall crystal (QAHC), and charge density wave (CDW) phases, demonstrating quantized Hall conductance in the topological phases. Analysis of real-space density distributions further reveals a √3 × √3 pattern consistent with a CDW, and a net charge of -1/3 associated with anyon halos, confirming their fractional nature.

Anyon Excitations and Charge Separation in MoTe2

Scientists have discovered robust FQAH ground states in twisted bilayer MoTe₂ through extensive numerical simulations, demonstrating the existence of anyon excitations, quasiparticles with fractional charge. Introducing a single electron into the FQAH state causes its charge to separate into three distinct regions, each carrying exactly 1/3 of the electron charge, unequivocally demonstrating the fractional nature of these excitations at a filling factor of −2/3. Detailed analysis of the real-space density distribution shows strong modulations within the anyons, aligning with the anyon density-wave halo picture, where internal modulation arises from proximity to a charge-ordered phase. A comprehensive phase diagram dependent on the displacement field applied to the material reveals a rich variety of charge-ordered states emerging from the FQAH phase, including an anomalous Hall crystal (QAHC) exhibiting integer quantized Hall conductance. The FQAH phase remains stable even with finite nearest-neighbor and next-nearest-neighbor interactions, and increasing the displacement field drives transitions into stripe and layer-polarized phases. Single-particle Green’s function measurements confirm insulating behavior in the stripe phase and metallic behavior in the layer-polarized phase, providing insights into the transport properties of these distinct phases.

Fractional Hall States and Anyon Excitations

This research presents a detailed computational study of FQAH states within twisted bilayer molybdenum ditelluride. Scientists employed large-scale simulations to demonstrate robust FQAH ground states and provide compelling evidence for the existence of anyon excitations, alongside characteristic density patterns consistent with theoretical predictions. The investigation reveals a complex relationship between the FQAH state and the emergence of charge-ordered phases, including an anomalous Hall crystal displaying integer quantized Hall conductance. The team mapped a comprehensive phase diagram dependent on an applied displacement field, uncovering a landscape of charge-ordered states originating from the FQAH state. Results indicate that the FQAH state and charge order do not simply compete, but instead intertwine through the internal structure of the system’s excitations, fundamentally reshaping its low-energy behaviour.