Graphene monolayers allow for relatively easy table-top realizations of relativistic quantum phenomena. In this talk, I study two examples for such effects.
First, by means of adatom deposition on graphene monolayers, it has become possible to experimentally study the supercriticality of the hydrogen bound state spectrum for 2D Dirac fermions.
We here discuss the related two-center problem which is defined by two nearby adatoms of opposite charge, forming an electric dipole. In the presence of a band gap, we show that there are infinitely many bound states induced by such an electric dipole. These states have a remarkable degree of universality known as Efimov scaling from the theory of the three-body bound state problem of bosons.
Second, in the presence of a magnetic field, a p-n junction in graphene harbors interesting interface states that semiclassically correspond to a stochastic sequence of snake-like orbits and skipping orbits. We here discuss the quantum mechanical solution of this problem.