  The effect of an inhomogeneous magnetic field which varies inversely as
distance on the ground state energy level of graphene is studied. In this work,
we analytically show that graphene under the influence of a magnetic field
arising from a straight long current-carrying wire ( proportional to the
magnetic field from carbon nanotubes and nanowires) exhibits zero energy
solutions. We find that contrary to the case of a uniform magnetic field for
which the zero energy modes show the localization of electrons entirely on just
one sublattice corresponding to single valley Hamiltonian, zero energy
solutions in this case reveal that the probability for the electrons to be on
the both sublattices, say A and B, are the same.
