Atomic Collapse in Graphene: Lost of Unitarity
  We explore the problem of atomic collapse in graphene by monopole impurities, both electric and magnetic, within the context of supersymmetric quantum mechanics. For electric impurities, upon factorizing the radial Dirac Hamiltonian and identifying the supercharges, existence of a critical charge that makes the ground state {\em fall-into-the-center} translates into lost of hermicity for the corresponding Hamiltonian and hence lost of unitarity of the theory. For the problem of magnetic monopole impurities, preservation of unitarity for all values of the parameters of the corresponding potential translates into the absence of atomic collapse in this case. 
David Valenzuela, Sa\'ul Hern\'andez-Ortiz, Marcelo Loewe and Alfredo   Raya
math-ph cond-mat.mes-hall hep-ph math.MP quant-ph