Aharonov-Bohm effect in clean strong topological insulator wires

Abstract

Surface electrons of strong topological insulator wires acquire a Berry phase difference of $\pi$ on orbiting the wire. This can be detected in response of clean wires (whose Fermi level is tuned to the Dirac point) to the presence of the Aharonov-Bohm flux. Specifically, at half-odd integer applied flux (in units of $hc/e$), long wires undergo semimetal-semiconductor transitions characterized by logarithmically divergent susceptibility. Associated with these are oscillations of magnetization (persistent current) that vanish both at integer and half-odd integer flux. Additionally wires of arbitrary aspect ratio exhibit conductance maxima at half-odd integer applied flux and minima at integer flux. For long wires the maxima are sharp with their height approaching $e^{2}/h$. Short wires are characterized by a universal conductivity $e^{2}/\pi h$ attained in the disc limit.