Zero-energy vortices in Dirac materials

In this brief review, we survey the problem of electrostatic confinement of massless Dirac particles, via a number of exactly solvable one- and two-body models. By considering bound states at zero energy, we present a route to obtain truly discrete states of massless Dirac particles in scalar potentials, circumventing the celebrated Klein tunnelling phenomenon. We also show how the coupling of two ultrarelativistic particles can arise, and discuss its implications for cutting-edge experiments with two-dimensional Dirac materials. Finally, we report an analytic solution of the two-body Dirac-Kepler problem, which may be envisaged to bring about a deeper understanding of critical charge and atomic collapse in mesoscopic Dirac systems.