Time-Reversal Invariant Topological Moir\'e Flatband: A Platform for the Fractional Quantum Spin Hall Effect

TL;DR

This paper proposes that moiré twisted bilayers of germanene and TMDs can host topologically nontrivial flatbands at small twist angles, providing a promising platform for realizing the fractional quantum spin Hall effect.

Contribution

It introduces a continuum model for moiré bilayers that predicts topological flatbands and demonstrates their potential to host fractional quantum spin Hall states with time-reversal symmetry.

Findings

Moiré flatbands can be topologically nontrivial due to inversion symmetry breaking.

Flatbands admit a lowest-Landau-level description in the chiral limit.

A many-body Laughlin state with time-reversal symmetry can be stabilized.

Abstract

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir\'e twisted bilayers with time-reversal symmetry and spin $s_z$ conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles, the emergent moir\'e flatbands can be topologically nontrivial due to inversion symmetry breaking. Each of these flatbands for each spin projection admits a lowest-Landau-level description in the chiral limit and at magic twist angle. This allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.