Edge-reconstruction in an interacting quantum spin Hall insulator

Theoretically "ideal" models of 2D topological insulators exhibit helical edge states that are protected against backscattering by time-reversal symmetry (TRS). However, in more realistic scenarios, where the confining potential at the boundary of the sample is shallow rather than sharp, edge reconstruction can occur, potentially leading to the breaking of TRS and interfering with the topological protection of the helical edge states [1]. Moreover, recent studies suggest that quantum fluctuations may restore TRS, and that even in the presence of random spin-orbit coupling, edge states recover their near-quantized conduction behavior [2]. To further study the interplay of quantum fluctuations and spontaneous TRS breaking, we performed large-scale DMRG calculations on ladders of a quantum spin Hall insulator, subjected to linear confinement in the presence of a full multi-orbital Hubbard interaction term, within the grand-canonical ensemble. A mean-field treatment allows us to identify a robust parameter regime exhibiting edge reconstruction which we analyze via DMRG calculations, probing the magnitude of magnetic moments in the reconstructed edge states which may have important consequences for dissipationless edge currents.

[1] J. Wang, Y. Meir, and Y. Gefen, Phys. Rev. Lett. 118, 046801 (2017)

[2] N. John, A. Del Maestro, and B. Rosenow, Europhysics Letters 140 26002 (2022)

[3] R. Soni, M. Thamm, B. Rosenow, G. Alvarez, and A. Del Maestro (in preparation)