Physics Research Conference

Most physicists are familiar with how nonrelativistic quantum mechanics governs the behavior of particles in simple potentials. But what happens when the particles become highly relativistic? Does their behavior change? Such questions used to lie mainly in the domain of high energy and nuclear physics. With the discovery that electrons in graphene behave like ultra-relativistic fermions, however, these questions are now accessible to the tools of condensed matter physics. I will describe experiments in which a scanning tunneling microscope (STM) was employed to manipulate charged atoms and molecules to construct various simple potentials in graphene. STM measurements were used to spectroscopically probe and visualize the resulting electronic wavefunctions of Dirac fermions in these potentials. We find that in the presence of a strong Coulomb potential graphene's massless electrons reorganize into "atomic collapse" states that are analogous to the bound states predicted for nuclei having atomic number greater than Z = 170. Fabrication of parabolic potentials allows us to observe quantum interference patterns that can be identified with the different principal and angular momentum quantum numbers of a relativistic simple harmonic oscillator. Atomically-precise one-dimensional arrays have also been fabricated via molecular self-assembly that allow visualization of a new class of extended supercritical states in graphene.