  We study the Aharonov-Bohm effect in an openended tube made of a graphene
sheet whose dimensions are much larger than the interatomic distance in
graphene. An external magnetic field vanishes on and in the vicinity of the
graphene sheet and its flux through the tube is adiabatically switched on. It
is shown that, in the process, the energy levels of the tight-binding
Hamiltonian of pi-electrons unavoidably cross the Fermi level, which results in
the creation of electron-hole pairs. The number of pairs is proven to be equal
to the number of magnetic flux quanta of the external field. The proof is based
on the new notion of partial spectral flow, which generalizes the ordinary
spectral flow already having well-known applications (such as the Kopnin forces
in superconductors and superfluids) in condensed matter physics.
