Local Probe of Bulk and Edge States in the Fractional Quantum Anomalous Hall Effect

Fractional quantum Hall effect (FQHE) is a prime example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order, and time reversal symmetry breaking. Recently, a lattice analog of FQHE at zero magnetic field has been observed, confirming the existence of a zero-field fractional Chern insulator (FCI). Despite this, the bulk-edge correspondence — a hallmark of FCI featuring an insulating bulk with conductive edges — has not been directly observed. In fact, this correspondence has not been visualized in any system for fractional states due to experimental challenges. In this talk, I will present our effort imaging of FCI edge states in twisted MoTe2 using microwave impedance microscopy. By tuning the carrier density, we observe the system evolving between metallic and FCI states, the latter of which exhibits insulating bulk and conductive edges as expected from bulk-boundary correspondence. Further analysis suggests the composite nature of the FCI edge states. We also observe the evolution of edge states across the topological phase transition as a function of interlayer electric field, and reveal tantalizing prospects of neighboring domains with different fractional orders. These findings pave the way for research into topologically protected 1D interfaces between various anyonic states at zero magnetic field, such as gapped 1d symmetry-protected phases with non-zero topological entanglement entropy, Halperin-Laughlin interfaces, and the creation of non-abelian anyons.