Atomic collapse in pseudospin-1 systems

We investigate atomic collapse in pseudospin-1 Dirac material systems whose energy band structure constitutes a pair of Dirac cones and a flat band through the conic intersecting point. We obtain analytic solutions of the Dirac-Weyl equation for the three-component spinor in the presence of a Coulomb impurity and derive a general criterion for the occurrence of atomic collapse in terms of the normalized strength of Coulomb interaction and the angular momentum quantum number. In particular, for the lowest angular momentum state, the solution coincides with that for pseudospin-1/2 systems, but with a reduction in the density of resonance peaks. For higher angular momentum states, the underlying pseudospin-1 wave functions exhibit a singularity at the point of zero kinetic energy. Divergence of the local density of states associated with the flat band leads to an inverse square type of singularity in the conductivity. These results provide insights into the physics of the two-body problem for relativistic quantum pseudospin-1 quasiparticle systems.