Mechanical and electronic properties of graphene under extrinsic conditions

학위논문(박사)--서울대학교 대학원 :자연과학대학 물리·천문학부,2016. 2. 임지순.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.I. Introduction 1 II. Tight-binding description of graphene and zigzag graphene nanoribbon 5 2.1 Basics 5 2.2 Tight-binding model description of graphene 7 2.3 Hubbard model description of zigzag graphene nanoribbons 13 III. Computational methods 17 3.1 Density functional theory 17 3.1.1 Hohenberg-Kohn theorem 18 3.1.2 Kohn-Sham formulation 21 3.1.3 Approximations for exchange-correlation energy 25 3.2 Pseudopotential plane wave approach 31 3.2.1 Plane wave basis set 31 3.2.2 Pseudopotential theory 34 3.2.3 Projector augmented method 41 3.3 Van der Waals interaction 43 3.4 Ab initio force constant methods 45 IV. Phonon softening and mechanical failure of graphene under tensile strain 51 4.1 Introduction 52 4.2 Calculation details 58 4.3 Results and discussion 58 4.3.1 Symmetry lowering strains and transition of phonon softening points 58 4.3.2 Crossover between two phonon instabilities 61 4.3.3 Phonon instability-driven mechanical failure 64 4.4 Conclusion 69 V. Investigation of graphene/hexagonal boron nitride double layer in regard to an STM experiment 71 5.1 Introduction 71 5.2 Calculation details 75 5.3 Results and discussion 77 5.3.1 Effect of substrates on STM simulation 77 5.3.2 Study of localized states at graphene zigzag edge 83 5.4 Conclusion 87 VI. Summary and perspectives 89 Bibliography 91 국문초록 103Docto