Tight binding investigation of graphene nanostructures under magnetic field

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2019
Yalçın, Fırat
Electrons moving under the effects of a two dimensional periodic potential and a magnetic field perpendicular to this two dimensional plane has been the focus of many different studies for a long time. The interplay between the two length scales in this problem, lattice constant and the characteristic magnetic length, results in interesting phenomena such as the Hofstadter's butterfly. The bulk of the studies done so far has focused on uniform magnetic fields. The only requirement for the vector potential is that its closed loop integral resulting in the correct flux piercing through the loop. This allows us to use a rather unconventional gauge where we set certain values for the line integrals instead of solving the line integrals with a known vector potential. Using this gauge, we can study the effects of inhomogeneous fields in a very efficient way. The electronic structures of hexagonal flakes, Y-shaped junctions and cross-shaped junctions of different sizes have been studied using tight-binding method and the optimal gauge. The results show emergence of new states around the Fermi level localized on the lattice sites where the magnetic fields are applied.
Citation Formats
F. Yalçın, “Tight binding investigation of graphene nanostructures under magnetic field,” M.S. - Master of Science, Middle East Technical University, 2019.