Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences


Physics and Astronomy

First Advisor

Dr. Ganpathy Murthy

Second Advisor

Dr. Ribhu K. Kaul


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 that explicitly lower the symmetry.

In the interacting case, we study the phases in the strong magnetic field limit. We consider on-site Hubbard and nearest-neighbor Heisenberg interactions. In the continuum limit, the theory has been studied by Kharitonov, who has found that there are four competing phases namely, ferromagnetic, antiferromagnetic, charge density wave, and Kekulé distorted phases. We find phase diagrams for q = 3, 4, 5, 6, 9, 12 where some of the phases found in the continuum limit are co-existent in the lattice limit. We also find phases not present in the continuum limit.

Digital Object Identifier (DOI)

Funding Information

NSF-DMR-1306897 (December 2017 - January 2018),

NSF-DMR-1611161 (May 2018 - August 2019)