Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene

Electrons in graphene, which behave as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a phenomenon in which discrete energy levels of superheavy atoms are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in graphene p–n junctions. We show how the transport problem in the presence of a magnetic field can be solved with the help of a Lorentz transformation, and use it to investigate magnetotransport in p–n junctions. Finally, we review a recent proposal to use Fabry–Pérot resonances in p–n–p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.