Edge density of bulk states due to relativity

TL;DR

This paper reveals that relativistic effects in Dirac materials like carbon nanotubes can cause boundary charge densities in bulk states, contrasting with non-relativistic wave functions, impacting their electronic properties.

Contribution

It demonstrates that relativistic bulk spinor states in Dirac materials can have non-zero boundary charge densities, a novel boundary effect linked to relativistic quantum mechanics.

Findings

Relativistic bulk states can have non-zero boundary charge density.

Contrast between relativistic and non-relativistic boundary wave functions.

Implications for transport and response to external fields.

Abstract

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.