Molecular collapse in monolayer graphene

Atomic collapse is a phenomenon inherent to relativistic quantum mechanics where electron states dive in the positron continuum for highly charged nuclei. This phenomenon was recently observed in graphene. Here we investigate a novel collapse phenomenon when multiple sub- and supercritical charges of equal strength are put close together as in a molecule. We construct a phase diagram which consists of three distinct regions: 1) subcritical, 2) frustrated atomic collapse, and 3) molecular collapse. We show that the single impurity atomic collapse resonances rearrange themselves to form molecular collapse resonances which exhibit a distinct quasi-bonding, anti-bonding and non-bonding character. Here we limit ourselves to a systems consisting of two and three charges. We show that by tuning the distance between the charges and their strength a high degree of control over the molecular collapse resonances can be achieved.