Observation of Yamaji Magic Angles in Bismuth Nanowires

Experimental studies that probe the surface of bulk bismuth as a composite of topological insulator edges and hinges on the surface of bulk Bi are lacking. We present angle-dependent transverse magnetoresistance (TMR) oscillation measurements of small diameter ( 50 nm ) bismuth nanowires where electronic transport is dominated by the surface, rather than the bulk in the core of the nanowire, because of quantum confinement. We find that the TMR of the surface states in our nanowires exhibits peaks for a sequence of nanowire rotation angles that strongly suggest an interpretation in terms of Yamaji magic angles. Magic angles are observed in layered and other low-dimensional conductors with weak interplanar coupling that are amenable to be described by an open, corrugated, Fermi surface. In contrast to surface states, bulk bismuth does not display magic angles since the Fermi surface is closed. We will discuss our interpretation of surface states of bismuth and the main Fermi surface parameters that we observe: orientation of the Fermi surface, Fermi wavevector, and coupling strength.