ArXiv · 2026
We predict and classify interaction-driven quantum spin Hall crystals (QSHCs), a class of states emerging at fractional filling through an interplay of topology and spontaneous translation-symmetry breaking. QSHCs form nearly degenerate manifolds whose members can realize distinct topological phases protected by time-reversal or valley U(1)ᵥ symmetry, with time-reversal acting nontrivially within the manifold. As a representative of this broad class of states we provide evidence for 9-fold quasi-degenerate √3×√3 charge ordered QSHCs at ν = -8/3 of twisted bilayer MoTe₂ near a 5^∘ twist. Here a Z₃ index organizes states related by lattice translation into three time-reversal invariant states with nontrivial Z₂ topology and three time-reversal related doublets whose individual members spontaneously break time-reversal and carry a U(1)ᵥ protected spin-Chern number. Finally, we determine the conditions that favor QSHCs over closely competing intervalley-coherent crystals.
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