Edge reconstruction in correlated quantum spin Hall insulators

Symmetry-protected helical edge states live at the boundary of a topologically non-trivial quantum spin Hall insulator. We consider a repulsive local interaction on each site of a two-dimensional ribbon and study the edge states upon increasing the Hubbard-$U$ strength.Due to its reduced coordination the surface has the tendency to become Mott insulating before the bulk. This activates a correlation-driven reconstruction mechanism in the intermediate-$U$ regime, before the whole system has become a Mott insulator itself. We analyze this phenomenon within the Bernevig-Hughes-Zhang model, which we solve by means of Dynamical Mean Field Theory at zero temperature [1-3]. Our results hints at viewing the influence of Coulomb interaction on the helical edge states from a combined bulk-edge perspective, challanging the customary approach based on model Hamiltonians with one spatial dimension by construction. \\ {[1]} A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel and G. Sangiovanni. {\it Phys.~Rev.~Lett.} {\bf 114}, 185701 (2015). \\ {[2]}A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel and G. Sangiovanni. {\it Phys.~Rev.~B} {\bf 93}, 235112 (2016). \\ {[3]} A. Amaricci, {\it et al.}, in preparation.