Transport discovery of emerging robust helical surface states in $Z_2=0$ systems

Abstract

We study the possibility of realizing robust helical surface states in $Z_2=0$ systems. We find that the combination of anisotropy and finite-size confinement leads to the emergence of robust helical edge states in both 2D and 3D $Z_2=0$ systems. By investigating an anisotropic Bernevig-Hughes-Zhang model in a finite sample, we demonstrate that the transport manifestation of the surface states is robust against non-magnetic disorder, resembling that of a $Z_2 = 1$ phase. Notably, the effective energy gap for the robust helical states can be efficiently engineered, allowing for potential applications as valley filters and valley valves. The realization of emerging robust helical surface states in realistic material is also discussed.