Low-dimensional systems : A quantum Monte Carlo study

Thomas, David and Drummond, Neil (2021) Low-dimensional systems : A quantum Monte Carlo study. PhD thesis, Lancaster University.

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Abstract

We study low-dimensional materials and devices through use of the variational and diffusion quantum Monte Carlo methods. Firstly, we use models of nanostructures in semiconductor heterostructures that confine charge-carriers in one (or more) dimensions to investigate the energetics of the charge-carrier complexes that form in such structures. For type-II quantum rings and superlattices, we present energy data to aid in experimental identification of these complexes and show that these energies are relatively insensitive to the geometrical dimensions of the devices. Secondly, we study similar models of charge-carrier complexes but this time where the confinement is provided by the two-dimensional nature of the material, rather than by artificial construction. Application of an in-plane electric field shifts the binding energies of complexes in monolayer transition metal dichalcogenides such that charged complexes can be identified from neutral ones. The truly two-dimensional character of these materials results in a Keldysh interaction between charge-carriers, rather than a screened Coulomb interaction. In such materials, modelling the two-dimensional electron gas using a more realistic Keldysh interaction acts to lower the Wigner crystallisation density, when compared to using a Coulomb interaction. Thirdly, and finally, we perform ab-initio calculations of the defect formation energy for mono-vacancies in graphene, with the aim of benchmarking the accuracy of the widely-used density functional theory method in these types of calculation. The mono-vacancy defect formation energy is shown to be significantly underestimated by density functional theory.