Gate-controlled one-dimensional channel on the topological surface

We investigate the formation of the one-dimensional channels on the topological surface under the gate electrode. The energy dispersion of these channels is almost linear in the momentum with the velocity sensitively depending on the strength of the gate voltage. The energy is also restricted to be positive or negative depending on the strength of the gate voltage. Consequently, the local density of states near the gated region has an asymmetric structure with respect to zero energy. In the presence of the electron-electron interaction, the correlation effect can be tuned by the gate voltage. We also suggest a tunneling experiment to verify the presence of these bound states.