Evolution of band structure and edge states upon increasing the spin splitting. (a) The spin-down states |E1, −⟩ and |H1, −⟩ in the same block of the Hamiltonian (Eq. (1) from Ref. [6]) touch each other and then enter the normal regime. In panel (b), the behavior of the edge states during the level crossing in the case of panel (a) is shown. Reprinted with permission from Ref. [9]. Copyright 2008 by the American Physical Society.