Moire driven edge reconstruction in Fractional quantum anomalous Hall states

TL;DR

This work shows that moiré lattice momentum constraints qualitatively reshape fractional edge physics in ν=2/3 FQAH states by enabling lattice-enabled umklapp processes. Using a moiré-adapted coupled-wire framework, the authors demonstrate two edge realizations with the same bulk order but different edge operator content, where one realization allows umklapp-assisted inter-edge tunneling and stabilizes the Kane–Fisher–Polchinski fixed point without disorder. The finite, two-edge system further reveals a topological pump of a 2e/3 quasiparticle whose momentum transfer aligns with Oshikawa’s commensurability, linking lattice geometry to anomaly structure. Together, these results highlight a lattice-driven route to edge reconstruction in fractional Chern insulators and offer a framework for interpreting edge transport in moiré FQAH systems.

Abstract

We investigate fractional edge modes in moire fractional quantum anomalous Hall states, focusing on the role of lattice momentum conservation and umklapp scattering. For the hierarchical nu=2/3 state, we show that, for a class of microscopic edge realizations, moire-enabled umklapp processes can stabilize the Kane-Fisher-Polchinski fixed point even in the absence of disorder.Our results illustrate how lattice momentum constraints can qualitatively reshape the interaction structure and low-energy behavior of fractional edge modes. The study of Umklapp processes in edge reconstruction serves as a crucial bridge to understanding thermal and electrical transport in the hierarchical fractional quantum anomalous Hall states found in lattice systems of quantum simulators.

Figures (3)

• Figure 1: Schematic illustration of a quantum-wire network defined on a moiré superlattice. The underlying moiré pattern has wavelength $\lambda = a_0/[2\sin(\theta/2)]$, set by the twist angle $\theta$. Three sets of parallel quantum wires are highlighted in distinct colors, forming a triangular network; within each set, neighboring wires are separated by a distance $d=\sqrt{3}\lambda/2$. While intra-set scattering processes play a central role in the coupled-wire construction discussed in the main text, scattering processes between different wire sets are subject to more stringent RG relevance conditions and can therefore be neglected at low energies hsu2023general.
• Figure 2: Schematic illustration of interwire tunneling processes leading to hierarchy $\nu=2/3$ states in the coupled-wire construction. In both panels, horizontal lines represent quantum wires and arrows indicate electron tunneling processes, following the standard coupled-wire notation kane2002fractionalteo2011luttinger.
• Figure S1: Schematic droplet picture of a finite-width $\nu=2/3$ FQHE wang2013edgewen2004quantum. The red arrows illustrate a topological pumping process that transfers a net charge $2e/3$ quasiparticle from the bottom edge to the top edge, composed of one $e$ mode and one $-e/3$ mode.