Author ORCID Identifier
Date Available
5-1-2020
Year of Publication
2020
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Physics and Astronomy
First Advisor
Dr. Ganpathy Murthy
Second Advisor
Dr. Ribhu K. Kaul
Abstract
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)
https://doi.org/10.13023/etd.2020.228
Funding Information
NSF-DMR-1306897 (December 2017 - January 2018),
NSF-DMR-1611161 (May 2018 - August 2019)
Recommended Citation
Das, Ankur, "GRAPHENE IN A UNIFORM MAGNETIC FIELD" (2020). Theses and Dissertations--Physics and Astronomy. 70.
https://uknowledge.uky.edu/physastron_etds/70
