Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs

TL;DR

This paper explains the emergence of magic angles and fractional Chern insulators in twisted homobilayer TMDs by mapping their continuum model to a Landau level problem, revealing conditions for topological flat bands.

Contribution

It introduces a novel mapping of the continuum model to a Landau level problem, clarifying the conditions for topological flat bands in twisted TMDs.

Findings

Quantum geometry is nearly ideal at specific flat-band twist angles.

Topological flat bands require strong valley-dependent moiré potential.

The approach provides a foundation for studying interactions in these systems.

Abstract

We explain the appearance of magic angles and fractional Chern insulators in twisted K-valley homobilayer transition metal dichalcogenides by mapping their continuum model to a Landau level problem. Our approach relies on an adiabatic approximation for the quantum mechanics of valence band holes in a layer-pseudospin field that is valid for sufficiently small twist angles and on a lowest Landau level approximation that is valid for sufficiently large twist angles. It simply explains why the quantum geometry of the lowest moir\'e miniband is nearly ideal at particular flat-band twist angles, predicts that topological flat bands occur only when the valley-dependent moir\'e potential is sufficiently strong compared to the interlayer tunneling amplitude, and provides a powerful starting point for the study of interactions