Aharonov-Bohm oscillations in disordered topological insulator nanowires

A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi$_2$Se$_3$ nanowires [Peng {\it et~al.}, Nature Mater.\ 2010] where conductance was found to oscillate as a function of magnetic flux $\phi$ through the wire, with a period of $h/e$ and {\it maximum} conductance at zero flux. This seemingly agrees neither with diffusive theory (period of $h/2e$) nor with ballistic theory, which in the simplest form predicts a period of $h/e$ but a {\it minimum} at zero flux due to a nontrivial Berry phase. We show how the magneto-conductance depends on doping and disorder strength, provide a possible explanation for the experiments, and discuss further experiments that could verify the theory.