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

TL;DR

This study visualizes and characterizes edge states in a fractional Chern insulator using microwave-impedance microscopy, confirming bulk-edge correspondence and observing topological phase transitions in twisted MoTe2.

Contribution

It introduces a new local imaging technique to directly observe FCI edge states and bulk-boundary correspondence in a zero-field system.

Findings

Imaging of FCI edge states in twisted MoTe2.

Observation of bulk-insulating and edge-conducting states.

Detection of topological phase transitions with electric field.

Abstract

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. Here we report the imaging of FCI edge states in twisted MoTe2 by employing a newly developed modality of 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. We also observe the evolution of edge states across the topological phase transition from an incompressible Chern insulator state to a metal and finally to a putative charge ordered insulating state as a function of interlayer electric field. The local measurement further reveals 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 topological entanglement entropy, Halperin-Laughlin interfaces, and the creation of non-abelian anyons.