How can quantum Hall physics exist without magnetic fields?

The fractional quantum Hall effect is one of the most striking manifestations of strong electronic correlations and topology, traditionally requiring intense magnetic fields. Recently, experiments reported the first observation of its magnetic-field-free counterpart—the fractional quantum anomalous Hall effect, also known as a fractional Chern insulator (FCI)—in twisted MoTe₂, a moiré material formed by stacking two layers of MoTe₂ with a small twist angle.

Motivated by this breakthrough, a joint team from the Institute of Theoretical Physics, Chinese Academy of Sciences and the National High Magnetic Field Laboratory in the United States has carried out a comprehensive theoretical investigation of this system. Using large-scale tensor network calculations based on a realistic real-space model constructed from Wannier orbitals, the researchers obtained a detailed ground-state phase diagram and systematically studied its finite-temperature and dynamical properties.

The calculations reveal that the twisted MoTe₂ undergoes a spontaneous ferromagnetic transition below a crtitical temperature and hosts a rich variety of correlated quantum phases. They include fractional Chern insulators, generalized Wigner crystal states, and quantum anomalous Hall crystals (QAHCs). Notably, QAHCs maintain quantized Hall conductance even at fractional electronic fillings, a phenomenon that has recently been observed in several experiments.

By simulating single-particle spectral functions, the study further identifies characteristic spectroscopic signatures of these exotic phases. Fractional Chern insulators display continua associated with fractionalized excitations, while quantum anomalous Hall crystals show clear band-folding features resulting from spontaneous lattice translation symmetry breaking.

Importantly, the finite-temperature analysis yields three key energy/temperature scales in this system: the ferromagnetic transition temperature, the thermal activation energy, and the charge gap. The results naturally explain the experimentally observed separation between the charge gap and thermal activation energy, providing a unified framework to interpret existing measurements and guiding future experiments aimed at controlling fractional quantum phases in moiré materials.

This work advances our understanding of fractional quantum Hall physics in moiré materials and establishes twisted MoTe₂ as a versatile platform for studying strongly correlated topological states under experimentally accessible conditions.

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