Supercritical electric dipole and migration of electron wave function in graphene

Abstract: We study the Dirac equation for quasiparticles in gapped graphene with two oppositely charged impurities by using the technique of linear combination of atomic orbitals and variational Galerkin--Kantorovich method. We show that for sufficiently large charges of impurities the wave function of the occupied electron bound state of the highest energy changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities increases. This migration of the electron wave function of supercritical electric dipole is a generalization of the familiar phenomenon of the atomic collapse of single charged impurity to the case where electron-hole pairs are spontaneously created from vacuum in bound states with charge impurities thus partially screening them.