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The fractional quantum Hall effect (FQHE) is a canonical example of a strongly interacting topological phase, where electron correlations, topology, and broken time-reversal symmetry give rise to anyons and chiral edge modes. Recently, a lattice analog of the FQHE at zero magnetic field, a fractional Chern insulator (FCI), has been realized in moiré materials. Theory predicts an insulating bulk with conducting fractional edge channels, but this bulk–edge structure has never been directly imaged for any fractional state, in either Landau-level or lattice systems.

In this talk, I will describe how we use microwave-impedance microscopy, a local GHz probe that senses complex conductivity at the nanoscale, to image edge states in a zero-field FCI realized in twisted MoTe₂. Spatially resolved measurements reveal conducting edges surrounding an insulating bulk, and indicate neighboring domains with different fractional orders. These results open the door to engineering and probing topologically protected 1D interfaces between distinct anyonic phases at zero field, with implications for tools such as Halperin–Laughlin interfaces, topological entanglement entropy, and platforms for non-Abelian excitations.

In the second part of the talk, I will briefly discuss our recent efforts to push these ideas to millimeter-wave frequencies, using cavity-based techniques compatible with cryogenic and high-field environments. I will highlight how the same microwave and mm-wave toolbox familiar from superconducting qubits and AMO can be repurposed as sensitive probes of correlated and topological quantum materials.