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Magnetoelectronics at Edges in Semiconductor Structures: Helical Aharonov-Casher Edge States

It is shown that an Aharonov-Casher vector potential in a two-dimensional geometry can lead to helical edge states, and initial experimental results are presented. The Aharonov-Casher vector potential is the electromagnetic dual of the magnetic vector potential, and leads to traveling states at the sample edge in analogy to the integer quantum Hall effect. The helical edge states are predicted to appear in a narrow channel geometry with parabolic or sufficiently symmetric confinement potential. The present work discusses implications of the helical Aharonov-Casher edge states, experimental considerations in specific materials systems, and experimental quantum transport results in mesoscopic geometries.