Creation of planar charged fermions in Coulomb and Aharonov-Bohm potentials

The creation of charged fermions from the vacuum by a Coulomb field in the presence of an Aharonov--Bohm (AB) potential are studied in 2+1 dimensions. The process is governed by a (singular) Dirac Hamiltonian that requires the supplementary definition in order for it to be treated as a self-adjoint quantum-mechanical operator. By constructing a one-parameter self-adjoint extension of the Dirac Hamiltonian, specified by boundary conditions, we describe the (virtual bound) quasistationary states with "complex energy" emerging in an attractive Coulomb potential, derive for the first time, complex equations (depending upon the electron spin and the extension parameter) for the quasistationary state "complex energy". The constructed self-adjoint Dirac Hamiltonians in Coulomb and AB potentials are applied to provide a correct description to the low-energy electron excitations, as well as the creation of charged quasiparticles from the vacuum in graphene by the Coulomb impurity in the presence of AB potential. It is shown that the strong Coulomb field can create charged fermions for some range of the extension parameter.Comment: 10 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1305.204

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in the QED$_{2+1}$ at the finite chemical potential, find the imaginary part of this Green function and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem to be likely to be revealed in a monolayer graphene sample in the presence of external constant uniform magnetic field $B$ perpendicular to it.Comment: 9 pages, 2 references are delete

Plane density of induced vacuum charge in a supercritical Coulomb potential

An expression for the density of a planar induced vacuum charge is obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in this potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. The behavior of the obtained vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulomb impurity in graphene is briefly discussed. We calculate the real vacuum polarization charge density that acquires the quantum electrodynamics vacuum in the supercritical Coulomb potential due to the so-called real vacuum polarization. It is shown that the vacuum charge densities essentially differ in massive and massless cases. We expect that our results can, as a matter of principle, be tested in graphene with a supercritical Coulomb impurity.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1601.0766