Quantum confinement in Dirac-like nanostructures

Abstract

In Westminster Abbey, in a nave near to Newton’s monument, lies a memorial stone to Paul Dirac. The inscription on the stone includes the relativistic wave equation for an electron: the Dirac equation. At the turn of the 21st century, it was discovered that this eponymous equation was not simply the preserve of particle physics. The isolation of graphene by Andre Geim and Konstantin Novoselov in Manchester led to the exploration of a novel class of materials – Dirac materials - whose electrons behave like Dirac particles. While the mobility of these quasi-relativistic electrons is attractive from the perspective of potential ultrafast devices, it also presents a distinct challenge: how to confine Dirac particles so as to avoid making inherently leaky devices? Here we discuss the unconventional quantum tunnelling of Dirac particles, we explain a strategy to create bound states electrostatically, and we briefly review some pioneering experiments seeking to trap Dirac electrons.