Study On Transport Properties Of Topological Insulators In Monoliths

In this thesis we discuss the theoretical calculation method of the quantum transport problems based on the ab-initio modeling, and apply this method on several transport models in molecule electronics, such as the2-D graphene nanoribbon p-n junction. This calculating method is based on the Landauer-Buttiker and the non-equilibrium Green function formalisms, which ensure the reliability and accuracy of the transport calculations. It can include the first, second and third nearest neighbor interactions, spin-orbit interaction and Rashba interaction. This method can be easily applied to many different molecule models in order to solve the transport problems. We use the new method to calculate the Green function and self-energy in order to avoid the traditional time-consuming consistency iteration, which has a huge advantage of efficiency. The calculation of the transport problems of the molecule components can theoretically reveal the electronic properties of the molecule components, which may help us deeply understand the mechanism of the quantum effects (such as quantum spin Hall effect) and contribute to the molecule electronic components design as well as the research of the quantum transport theory. In the thesis we calculate the conductance vs voltage curve of the graphene nanoribbon p-n junction by taking account of the first, second and third nearest neighbor interactions, spin-orbit interaction and Rashba interaction. We study the phase transition of the graphene p-n junction among the conducting phase, insulating phase and QSH (quantum spin Hall) phase by calculating the phase diagram of conductance, which shows that the graphene p-n junction model is a topological insulator.This article is organized as follows:Chapter1:The background and introduction of the molecule electronics.Chapter2:Introduction and review of the development of the ab-initio calculating method based on Landauer-Biittiker formalism and non-equilibrium Green function. The detailed calculation framework will be given.Chapter3:Introduction and study of the graphene nanoribbon p-n junction by calculating its conductance to reveal the topological insulator features. Our calculation of the conductance curves suggest that quantum spin Hall effect can happen in the graphene p-n junction even without any magnetic field, which match the experiments and prediction based on the energy-band theory. By the comparison among the first, second and third nearest neighbor interactions, we prove that the second nearest neighbor interaction in the topological insulators plays a crucial role in the mechanism of the quantum spin Hall effect.