Exciton dispersions in two-dimensional materials - Li, Yifei (Nanyang Technological University, 2023)
This thesis is dedicated to the calculation of a numerically solvable form of the Hamiltonian excitons in 2D materials. 2D materials are quite new, having only been fully realised only about 20 years ago[2][4].Theoretical predictions had been made about the existence of these materials for many years, with experiments going back to the 1960s[1]. As the area is quite new, numerical solutions are particularly useful as it not only allows using computers to quickly predict the properties of such materials, but also gives a check on if the experiment is done correctly. In this thesis, I will attempt to solve for a Hamiltonian for excitons in a 2D material. The problem was tackled by noting what contributes to the Hamiltonian, then solving the obtained expressions. The results from the calculations are then constructed in a form that is easy to implement and calculate via computer code such as Numpy. Some simplifications are also done to reduce the computational resource requirements. The resultant solution is of a generic form, as no specific parameters are defined in the thesis. This allows for flexibility in substituting in the desired parameters.