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

Abstract

Motivated by recent experimental observation of the quantum spin Hall effect in monolayer germanene, we study the topological phases of twisted bilayer Kane-Mele model with time-reversal symmetry and spin $s_z$ conservation. For large twist angles the helical edge states from the two layers are unstable and the system is a trivial insulator. At small twist angles however, the emergent moir\'e flatbands can be topologically nontrivial due to inversion symmetry breaking from coupling to substrate. 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