  The boundaries of quantum materials can host a variety of exotic effects such
as topologically robust edge states or anyonic quasiparticles. Here, we show
that fermionic systems such as graphene that admit a low energy Dirac
description can exhibit counterintuitive relativistic effects at their
boundaries. As an example, we consider carbon nanotubes and demonstrate that
relativistic bulk spinor states can have non zero charge density on the
boundaries, in contrast to the sinusoidal distribution of non-relativistic wave
functions that are necessarily zero at the boundaries. This unusual property of
relativistic spinors is complementary to the linear energy dispersion relation
exhibited by Dirac materials and can influence their coupling to leads,
transport properties or their response to external fields.
