Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect

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 moiré 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 moiré 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.

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• Non-Abelian spin Hall insulator
• Possible Sliding Regimes in Twisted Bilayer WTe${}_2$
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Variational wavefunctions for fractional topological insulators
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Time-dependent conserved operators for autonomous systems and quantization of resistance