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Electrical control of spin dynamics in Bi$_{\rm 2}$Se$_{\rm 3}$ wasinvestigated in ring-type interferometers. Aharonov-Bohm andAltshuler-Aronov-Spivak resistance oscillations against magnetic field, andAharorov-Casher resistance oscillations against gate voltage were observed inthe presence of a Berry phase of $\pi$. A very large tunability of spinprecession angle by gate voltage has been obtained, indicating that Bi$_{\rm2}$Se$_{\rm 3}$-related materials with strong spin-orbit coupling are promisingcandidates for constructing novel spintronic devices.

Aharonov-Casher effect in Bi$_{\rm 2}$Se$_{\rm 3}$ square-ring interferometers