TY - BOOK

T1 - Low-dimensional systems

T2 - A quantum Monte Carlo study

AU - Thomas, David

PY - 2021

Y1 - 2021

N2 - We study low-dimensional materials and devices through use of thevariational and diffusion quantum Monte Carlo methods. Firstly, weuse models of nanostructures in semiconductor heterostructures thatconfine charge-carriers in one (or more) dimensions to investigatethe energetics of the charge-carrier complexes that form in suchstructures. For type-II quantum rings and superlattices, we presentenergy data to aid in experimental identification of these complexesand show that these energies are relatively insensitive to thegeometrical dimensions of the devices.Secondly, we study similar models of charge-carrier complexes butthis time where the confinement is provided by the two-dimensionalnature of the material, rather than by artificial construction.Application of an in-plane electric field shifts the binding energiesof complexes in monolayer transition metal dichalcogenides such thatcharged complexes can be identified from neutral ones. The trulytwo-dimensional character of these materials results in a Keldyshinteraction between charge-carriers, rather than a screened Coulombinteraction. In such materials, modelling the two-dimensionalelectron gas using a more realistic Keldysh interaction acts to lowerthe Wigner crystallisation density, when compared to using a Coulombinteraction.Thirdly, and finally, we perform ab-initio calculations ofthe defect formation energy for mono-vacancies in graphene, with theaim of benchmarking the accuracy of the widely-used densityfunctional theory method in these types of calculation. Themono-vacancy defect formation energy is shown to be significantlyunderestimated by density functional theory.

AB - We study low-dimensional materials and devices through use of thevariational and diffusion quantum Monte Carlo methods. Firstly, weuse models of nanostructures in semiconductor heterostructures thatconfine charge-carriers in one (or more) dimensions to investigatethe energetics of the charge-carrier complexes that form in suchstructures. For type-II quantum rings and superlattices, we presentenergy data to aid in experimental identification of these complexesand show that these energies are relatively insensitive to thegeometrical dimensions of the devices.Secondly, we study similar models of charge-carrier complexes butthis time where the confinement is provided by the two-dimensionalnature of the material, rather than by artificial construction.Application of an in-plane electric field shifts the binding energiesof complexes in monolayer transition metal dichalcogenides such thatcharged complexes can be identified from neutral ones. The trulytwo-dimensional character of these materials results in a Keldyshinteraction between charge-carriers, rather than a screened Coulombinteraction. In such materials, modelling the two-dimensionalelectron gas using a more realistic Keldysh interaction acts to lowerthe Wigner crystallisation density, when compared to using a Coulombinteraction.Thirdly, and finally, we perform ab-initio calculations ofthe defect formation energy for mono-vacancies in graphene, with theaim of benchmarking the accuracy of the widely-used densityfunctional theory method in these types of calculation. Themono-vacancy defect formation energy is shown to be significantlyunderestimated by density functional theory.

KW - condensed matter theory

KW - quantum Monte Carlo

KW - excitons

KW - graphene

KW - TMDCs

KW - type-II semiconductors

U2 - 10.17635/lancaster/thesis/1457

DO - 10.17635/lancaster/thesis/1457

M3 - Doctoral Thesis

PB - Lancaster University

ER -