2D materials has become one of the most exciting areas of research, since the report of graphene in 2005. For graphene, the high mobility (∼ 15,000 cm2V−1s−1)draws much attention to its potential as high speed electronic devices. Its cone-like electronic dispersion, resembling that of relativistic massless Dirac fermions, entertains many exotic and interesting behaviors, making it an ideal system for the study of relativistic particles. Aside from graphene, many other 2D materials have also been successfully made, including MoS2, h-BN, 2D Boron, etc. Although these newly made materials have already exhibited several good characteristics, they are also distinctively different from traditional 3D materials. This means that a deeper understanding of 2D materials is imperative, to capture and utilize their unique features. The abundant atomistic modeling methods nowadays enable us to investigate the various aspects of 2D materials (or any system in general), with the help of computers. Density Functional Theory (DFT) based methods can give very accurate descriptions of the ground state properties of materials, including their charge density, mechanical moduli or the optimal structure; on top of DFT, many body theory methods also allow for the construction of excitation processes based on the DFT results. In the case of large structures, in which DFT may not be affordable, the tight-binding method can be an excellent alternative with a much lower cost.

In this work, I will employ these atomistic methods to the understanding of the distinctive features of 2D materials, especially their electronic, or even electro-mechanical properties. First, I have found that the graphite screw dislocations (GSD), a family of graphene-like structures as nanoribbons, turn out to be superior nano-solenoids, producing magnetic field up to 1T at typical voltage. Second, I have successfully modeled the strain-induced Landau quantization of the graphene band structure in large structures (N∼105), showing the possibility of strain engineering for the design of desired Landau levels in actual devices. Finally, I have discovered several universal features for 2D lateral junctions. 2D junctions, due to the weak electronic screening, turn out to be not merely a miniaturized version of its 3D counterpart. The scaling laws, depletion region and several practical consequences are analyzed and quantified.