Edge state reconstruction from strong correlations in quantum spin Hall insulators

We study the fate of helical edge states in a quantum spin Hall insulators when the whole system is exposed to strong Coulomb interactions. Using dynamical mean-field theory, we show that the dispersion relation of the edge states is strongly affected by Coulomb interactions. In fact, the formerly gapless edge modes become gapped at a critical interaction strength. Interestingly, this critical interaction strength is significantly smaller at the edge than its counterpart in the bulk. Thus, the bulk remains in a topologically nontrivial state at intermediate interaction strengths where the edge states are already gapped out. This peculiar scenario leads to the reconstruction of gapless helical states at the new boundary between the topological bulk and the trivial (Mott insulating) edge. Further increasing the interaction strength triggers the progressive localization on the new boundary, the shrinking of the quantum spin Hall region, and the migration of the helical edge states towards the center of the system. The edge state reconstruction process is eventually interrupted by the Mott localization of the whole sample. Finally, we characterize the topological properties of the system by means of a local Chern marker