  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 longitudinal magnetic field $B$ they lead to Aharonov-Bohm
amendment for the density of states and correspondingly for conductivity of the
nanowire. The phase of these magnetooscillations increases with $B$ from $\pi$
to $2\pi$.
