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

Gate-controlled one-dimensional channel on the topological surface