Time-reversal invariant topological moiré flat band: A platform for the fractional quantum spin Hall effect

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.