Aharonov—Bohm Oscillations in Small Diameter Bi Nanowires

Abstract

The Aharonov–Bohm effect (AB) exists in cylindrical wires as the magnetoresistance (MR) oscillations with a period ΔB that is proportional to Φ0 ∕ S, where Φ0 = h ∕ e is the flux quantum and S is the wire cross section. The AB-type longitudinal MR oscillations with period ΔB = Φ0 ∕ S caused by electrons undergoing continuous grazing incidence at the wire wall have been observed previously at 4.2 K in single bismuth nanowires with a diameter 0. 2 < d < 0. 8 μm grown by the Ulitovsky technique. We present here our results of the observation of AB oscillations with period ΔB = h ∕ e and ΔB = h ∕ 2e on single Bi nanowires with a diameter d = 45–73 nm. The single nanowire samples were prepared by improved Ulitovsky technique and represented cylindrical single crystals with (1011) orientation along the wire axis. Due to very low effective masses of electrons and holes, electronic quantum confinement effects induce a semimetal-to-semiconductor transformation (SMSC) for wires with diameters below 50 nm. Our estimation of thermal energy gap from R(T) dependence for 50 nm Bi wire gives the value of 14 meV. The surface of Bi nanowire supports surface states, with carrier densities of around 5 ×1012 cm− 2 with strong spin-orbit interactions. From B ∼ 8 T down to B = 0, the extremums of h/2e oscillations are shifted up to 3π at B = 0, which is the manifestation of Berry phase shift. We connect the existence of h ∕ 2e oscillations with weak localizations on surface states of Bi nanowires according to the Altshuller–Aronov–Spivak theory.