In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are studied. For localized near plane Dirac particle the expression for current, charge and density are presented. For bound state with massless dispersion law the current, charge and density are calculated for simplified model with 2 parameter exactly.The model can find application to a wide class of phenomena arising by the interaction of fields of quantum electrodynamics with two-dimensional materials.