Aharonov-Bohm oscillations caused by non-topological surface states in Dirac nanowires

One intriguing fingerprint of surface states in topological insulators is the Aharonov-Bohm effect in magnetoconductivity of nanowires. We show that surface states in nanowires of Dirac materials (bismuth, bismuth antimony, and lead tin chalcogenides) being in non-topological phase, exhibit the same effect as amendment to magnetoconductivity of the bulk states. We consider a simple model of a cylindrical nanowire, which is described by the 3D Dirac equation with a general $T$-invariant boundary condition. The boundary condition is determined by a single phenomenological parameter whose sign defines topological-like and non-topological surface states. The non-topological surface states emerge outside the gap. In a longitudinal magnetic field $B$, they lead to Aharonov–Bohm amendment for the density of states and correspondingly for the conductivity of the nanowire. The phase of these magnetic oscillations increases with $B$ from $\pi$ to $2\pi$.