Visualizing the Behavior of Relativistic Electrons in Simple 2D Potentials in Graphene
Abstract: Although most physicists understand how nonrelativistic particles behave in Coulomb and harmonic oscillator potentials, the case for relativistic particles is much less familiar. Graphene, with charge carriers that act like massless Dirac fermions, provides a convenient platform for studying ultra-relativistic quantum mechanics. In this talk, I will describe scanning tunneling microscopy (STM) experiments in which charged impurities on gate-tunable graphene were manipulated to build Coulomb and harmonic oscillator potentials. For a Coulomb potential, we find that graphene's Dirac electrons form "atomic collapse" states that are highly analogous to the expected bound states of nuclei with atomic number Z > 137. For a harmonic oscillator potential, we observe the electrostatic confinement of ultra-relativistic fermions, which produces quantum interference patterns for various principal and angular momentum quantum numbers.