Electronic structure calculations of in-plane bent graphene nanoribbons

Abstract

The electronic properties of graphene are influenced by both geo- metric confinement and strain. In this thesis, we study the electronic structure of in-plane bent graphene nanoribbons, a confined strained graphene system. We develop a tight-binding model that has a small computational cost and is based on three parameters: hopping, overlap and an exponential decay rate. This model predicts that the bandgap of armchair graphene nanoribbons after bending behaves similarly to the bandgap after a uniform longitudinal strain, and in general is not very sensitive to bending. However, it also predicts that the edge states within zigzag graphene nanoribbons are sensitive to bending and develop an effective 1D chain dispersion. Because the slope of the dispersion is connected to the velocity of the electrons at the edge, this means that the edge states change from localized to delocalized upon increasing the degree of bending. We also take the first steps in an analysis of bent graphene nanoribbons using the massless Dirac fermion continuum de- scription of graphene by combining boundary conditions and a pseudo- magnetic field.