  The interface between a solid and vacuum can become electronically distinct
from the bulk. This feature, encountered in the case of quantum Hall effect,
has a manifestation in insulators with topologically protected metallic surface
states. Non-trivial Berry curvature of the Bloch waves or periodically driven
perturbation are known to generate it. Here, by studying the angle-dependent
magnetoresistance in prismatic bismuth crystals of different shapes, we detect
a robust surface contribution to electric conductivity when the magnetic field
is aligned parallel to a two-dimensional boundary between the three-dimensional
crystal and vacuum. The effect is absent in antimony, which has an identical
crystal symmetry, a similar Fermi surface structure and equally ballistic
carriers, but an inverted band symmetry and a topological invariant of opposite
sign. Our observation points to the relevance of band symmetries to survival of
metallicity at the boundary interrupting the cyclotron orbits.
