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

Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a novel state of superheavy atoms stripped of their discrete energy levels, which 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 another system, graphene p-n junctions. We show how the transport problem in the presence of 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 recent proposal to use Fabry-Perot resonances in p-n-p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.