1307.7728 (E. V. Gorbar et al.)

Supercritical instability in graphene with two charged impurities    [PDF]

E. V. Gorbar, V. P. Gusynin, O. O. Sobol

We study the supercritical instability in gapped graphene with two charged impurities separated by distance R using the two-dimensional Dirac equation for electron quasiparticles. The attention is paid to a situation when charges of impurities are subcritical whereas their total charge exceeds a critical one. The critical distance R_{cr} in the system of two charged centers is defined as that at which the electron bound state with the lowest energy reaches the boundary of the lower continuum. A variational calculation of the critical distance R_{cr} separating the supercritical (RR_{cr}) regimes is carried out. It is shown that the critical distance R_{cr} increases as the quasiparticle gap decreases. The energy and width of a quasistationary state as functions of the distance between two impurities are derived in the quasiclassical approximation.

View original: http://arxiv.org/abs/1307.7728