Novel Quantum Devices and Innovative Simulation Methods for Quantum Engineering

Advances in the discovery and fabrication of 2D materials in the last few decades have opened new avenues of research for their application. Their inherent 2D nature makes these materials and their properties more sensitive to quantum effects, and therefore amenable to quantum engineering and the development of novel devices. These materials and resulting quantum systems therefore require new simulation methods and techniques to determine their viability in various applications. In this PhD dissertation a review of two novel quantum devices, which have been published previously, will be discussed. Additionally, extensions to the Finite Difference Method (FDM) which may be used in the study and design of future quantum systems more generally will also be explored. The specific devices that will be discussed are mixed-dimensional Resonant Tunneling Devices (RTDs) and Nano-Chevron Quantum Dots (NC-QDs). Regarding the extension of the FDM, methods for including Spin-Orbit Coupling (SOC) and self-consistent solutions to the Poisson-Schrödinger system of equations will be discussed.