Data from: Local probe of bulk and edge states in a fractional Chern insulator

Fractional quantum Hall effect (FQHE) is a prime example of topological
quantum many-body phe- nomena, 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. Here we
report the 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.