Theoritical study of quantum transport

Abstract

This thesis presents a theoretical study of electron transport in small electronic devices, especially Single-Electron Transistors (SETs) and quantum dots (QDs). At very small sizes, traditional electrical behavior changes, and new effects like tunneling, charge quantization, and Coulomb blockade become important. These effects help explain how electrons move one at a time in controlled ways, which is useful for building energy-efficient and highly sensitive devices. The work starts by examining SETs with metallic islands, where electron flow is blocked or allowed based on the charging energy and the applied gate voltage. Then, it focuses on quantum dots, which are even smaller regions where electrons are confined, leading to discrete energy levels. The study shows how gate voltage can tune the energy levels and control the flow of electrons through the device. The resulting patterns, called Coulomb diamonds, are explained using simple energy models. Later sections explore more complex processes such as co-tunneling and the Kondo effect. These occur when electrons interact strongly or when regular tunneling is blocked. These processes change how current flows through the device, especially at very low temperatures. The thesis also discusses thermal transport in Single-Electron Devices, where not only charge but also heat is carried by electrons. It explains how heat transfer is influenced by factors like charging energy, gate voltage, and temperature. The study shows that under certain conditions, classical laws such as the Wiedemann– Franz law do not hold. These findings are important for understanding energy flow in nanoscale systems and can help in designing low-power and thermally efficient devices. The models and concepts discussed in this work are supported with mathematical analysis and diagrams to improve understanding. Although the study is theoretical, it connects closely with experimental observations. Overall, this thesis provides a strong foundation for understanding electron and thermal transport in nanoscale systems and supports future research in nanoelectronics and device design.