  The influence of a topological defect in graphene on the ground state of
electronic quasiparticle excitations is studied in the framework of the
long-wavelength continuum model originating in the tight-binding approximation
for the nearest neighbour interaction in the graphitic lattice. A topological
defect that rolls up a graphitic sheet into a nanocone is represented by a
pointlike pseudomagnetic vortex with a flux which is related to the deficit
angle of the cone. The method of self-adjoint extensions is employed to define
the set of physically acceptable boundary conditions at the apex of the
nanocone. The electronic system on a graphitic nanocone is found to acquire the
ground state condensate and current of special type, and we determine the
dependence of these quantities on the deficit angle of the nanocone, continuous
parameter of the boundary condition at the apex, and the distance from the
apex.
