Theoretical Research On The Topology And Transportation Characteristics Of Semiconductor Quantum Dots

Quantum dots is an important zero-dimensional semiconductor systems,subjected to strong confinement along all the three spacial directions,similar to atoms and molecules in nature.Consequently,semiconductor quantum dots exhibit many distinct physical properties that have wide applications in nonlinear optics,medical science,functional materials,spintronics,and quantum informa-tion.In recent years,it has attracted a widespread interest from the scientific community.In this thesis,we perform theoretical study on the topological prop-erties and transport properties of semiconductor quantum dots.(1)Topological insulators is a new quantum state of the matter,which is gapped in the bulk but has gapless edge states on the surface.The existence of these novel edge states are protected by the nontrivial topology and the time-reversal symmetry and have many potential applications.These applications depend crucially on the robustness of the edge states against external perturbations.However,in recent years,there are very few quantitative study on this issue.In the thesis,we quantify the robustness of the topological edge states against a commonly encountered external perturbation-electric field.Our results demonstrate that the topological edge states are much more robust than the conventional bulk states of the quantum dot,thus establishing the advantange of topological quan-tum dots over conventional ones.(2)The distinct transport properties of the quantum dots form the physical basis of its various applications.The electron shuttle as an important research direction of quantum dot transport has received a lot of attention recently.However,there lack a systematic study on the dynam-ical location of interacting electrons in the quantum dot shuttle.In particular,the analytical condition for the appearance of dynamical localization remains unclear.Here we study the shuttle of interacting electrons in three quantum dots and reveal the influence of electron-electron Coulomb interaction and the vibration on the dynamical localization under ac electric field.This thesis involves many concepts about the energy bands of semiconduc-tors and their nanostructures,so we first introduce two important theoretical tools to describe the electronic states of semiconductor nanostructures:the tight-binding model(which helps us to visualize the formation of the energy band)and the effective-mass theory.Next we introduce the basic concepts of topological insulators and semiconductor quantum dots,as well as our theoretical study on the response of the electronic states in topological insulator quantum dots to a perturbative external electric field.Then we introduce our study on the dynami-cal localization of the electron shuttle in three quantum dots driven by ac electric field.Finally,we give the summary and outlook.This thesis consists of the following five chapters:The first chapter is the introduction,which describes the energy band theory and the research background.The second chapter introduces our study on the robustness of the electronic state of a topological insulator quantum dot against perturbative electric field.The existence of the edge states is an important manifestation of the nontrivial topology of topological insulators and is an important aspect for the applica-tion of this novel material.Here for the first time we quantify the robustness of the topological edge states in quantum dots against external electric field and demonstrate the robustness of the topological edge states compared with the con-ventional bulk states.Our study paves the way towards utilizing the topological quantum dots for various applications.The third chapter is the study of the electronic states in anomalous quantum Hall insulator quantum dots.The fourth chapter is the study of the dynamic localization of two interacting electrons in triple quantum dots and quantum dot shuttles induced by alternating current electric fields.We found that the introduction of the Coulomb interac-tion will increase the dynamic localization under certain conditions.Moreover,the mechanical vibration of quantum dot shuttles will also affect the dynamic localization.We derive the analytical condition of two-electron localization both for triple quantum dots and quantum dot shuttles.In the last chapter,we make a summary for the above work and give an outlook of the future study.