Mechanical and electronic properties of graphene under extrinsic conditions

Abstract

Since the groundbreaking experiments in 2004, the following years have been the era of graphene, a two-dimensional material. Graphene has been an exciting playground for both theorists and experimentalists due to its two-dimensional nature and the fascinating material properties. Although many theoretical studies have been performed on the ideal form of graphene in the limit of an infinite lattice, in real experimental situations, however, what we encounter are apart from those theoretically expected from the ideal graphene. Therefore, aside from revealing the intrinsic properties of graphene, it is also important to expect the changes of its properties under extrinsic conditions. Meanwhile, those deviations may come from the existence of edge or boundary, the substrate-induced stress, and the electronic hybridization with substrates. An encounter with edge or boundary is inevitable in real situations, but there is a still room for refining it. Moreover, a removal of the substrate-induced degradation and an improvement of experimental environments can be achieved by choosing the right substrates. With those facts in mind, in this thesis we focus on the mechanical and electronic properties of graphene under extrinsic conditions. In the first part, mechanical properties of graphene under general tensile strain are studied. Ab initio force constant method is adopted to calculate phonon dispersions with the usual first-principles calculations. We show the transition of Kohn anomaly points from a high-symmetry k point to a lower-symmetry one under the symmetry-lowering tensile strain, which can be interpreted in relationship to the Dirac point shift in the electronic structure. We demonstrate that the strain-induced enhancement of phonon softening can give rise to phonon instabilities over a wide range of tensile strain directions, resulting in a mechanical failure of graphene at lower strains. In addition, we show that there are two types of instabilities leading to mechanical failure prior to the elastic failure. In the second part, electronic properties of epitaxially grown graphene/hexagonal boron nitride double layer are studied in regard to a scanning tunneling microscopy experiment. Scanning tunneling microscopy simulations based on first-principles calculations are performed to identify the sample on which the measurements were conducted in the experiment. We demonstrate the limitation of such measurement on graphene directly contacting with metal substrates. We also clarify the role of hexagonal boron nitride monolayer in the system by showing the differences in the projected density of states and decaying patterns of charge densities with and without the layer. In addition, we investigate the zigzag edge localized state of graphene on h-BN monolayer with low-energy effective Hamiltonian and reproduce the experimental results. Finally, we summarize this thesis and present perspectives for further exploration.