Home > Research > Publications & Outputs > Low-dimensional systems

Associated organisational unit

Electronic data

  • 2021thomasphd

    Final published version, 8.58 MB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Text available via DOI:

View graph of relations

Low-dimensional systems: A quantum Monte Carlo study

Research output: ThesisDoctoral Thesis

Publication date2021
Number of pages156
Awarding Institution
Award date18/10/2021
  • Lancaster University
<mark>Original language</mark>English


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

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.