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 & eacute; 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 & eacute; flat bands can be topologically nontrivial due to inversion symmetry breaking. Each of these flat bands admits a lowest -Landau -level description for each spin projection 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.