Edge density of bulk states due to relativity

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 nonzero charge density on the boundaries, in contrast to the sinusoidal distribution of nonrelativistic 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.