  There are two types of intrinsic surface states in solids. The first type is
formed on the surface of topological insulators. Recently, transport of
massless Dirac fermions in the band of "topological" states has been
demonstrated. States of the second type were predicted by Tamm and Shockley
long ago. They do not have a topological background and are therefore strongly
dependent on the properties of the surface. We study the problem of the
conductivity of Tamm-Shockley edge states through direct transport experiments.
Aharonov-Bohm magneto-oscillations of resistance are found on graphene samples
that contain a single nanohole. The effect is explained by the conductivity of
the massless Dirac fermions in the edge states cycling around the nanohole. The
results demonstrate the deep connection between topological and non-topological
edge states in 2D systems of massless Dirac fermions.
