Vladimir Nazaikinskii - Microlocal and Global A...
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Vladimir Nazaikinskii - Microlocal and Global Analysis, Interactions with Geometry
Partial Spectral Flow and the Aharonov-Bohm Effect in Graphene.
Consider a graphene tube in the shape of a right circular open-ended cylinder whose height and radius
are both much greater than the distance between neighboring carbon atoms. A magnetic eld everywhere vanishing
on the tube surface (or at least tangent to it) is adiabatically switched on, causing the eigenvalues of the tightbinding
Hamiltonian describing the electron -states in graphene in the nearest neighbor approximation to move in
the process. If the magnetic
ux through the tube in the nal conguration has an integer number of
then the nal Hamiltonian is unitarily equivalent to the initial one, and hence the electron energy spectrum returns
to its original position. Moreover, the lattice function space on which the tight-binding Hamiltonian acts being
nite-dimensional, the spectral
ow of the Hamiltonian, dened as the net number of eigenvalues (counted with
multiplicities) that pass through