Electric-field modulation of the number of helical edge states in thin-film semiconductors

We propose a method that can be used to modulate the topological orders or the number of helical edge states in ultrathin-film semiconductors without a magnetic field. By applying a staggered periodic potential, the system undergoes a transition from a topological trivial insulating state into a nontrivial one with helical edge states emerging in the band gap. Further study demonstrates that the number of helical edge states can be modulated by the amplitude and the geometry of the electric potential in a stepwise fashion, which is analogous to tuning the integer quantum Hall conductance by a magnetic field. We address the feasibility of experimental measurement of this topological transition.