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Graphene In A Uniform Magnetic Field, Ankur Das

Theses and Dissertations--Physics and Astronomy

We study monolayer graphene in a uniform magnetic field in the absence and presence of interactions. In the non-interacting limit, for p/q flux quanta per unit cell (p, q are coprime integer), the central two bands have 2q Dirac points in the Brillouin zone (BZ) in the nearest-neighbor model. These touchings and their locations are guaranteed by chiral symmetry and the lattice symmetries of the honeycomb structure. If we add a staggered potential and a next-nearest-neighbor hopping we find that their competition leads to a topological phase transition. We also study the stability of the Dirac touchings to one-body perturbations …