TY - BOOK

T1 - Low-dimensional quantum systems

AU - Szyniszewski, Marcin

PY - 2016

Y1 - 2016

N2 - We study low-dimensional quantum systems with analytical and computational methods. Firstly, the one-dimensional extended t-V model of fermions with interactions of finite range is investigated. The model exhibits a phase transition between liquid and insulating regimes. We use various analytical approaches to generalise previous theoretical studies. We devise a strong coupling expansion to go beyond first-order perturbation theory. The method is insensitive to the presence or the lack of integrability of the system. We extract the ground state energy and critical parameters of the model near the Mott insulating commensurate density. A summary of the methods used is provided to give a broader view of their advantages and disadvantages.We also study the possible charge-density-wave phases that exist when the model is at the critical density. A complete description of phase diagrams of the model is provided: at low critical densities the phases are defined analytically, and at higher critical densities we tackle this problem computationally. We also provide a future outlook for determining the phases that occur at non-zero temperature.Secondly, we investigate Mott-Wannier complexes of two (excitons), three (trions) and four (biexcitons) charge carriers in two-dimensional semiconductors. The fermions interact through an effective interaction of a form introduced by Keldysh. Our study also includes impurity-bound complexes. We provide a classification of trions and biexcitons in transition-metal dichalcogenides, which incorporates the difference of spin polarisation between molybdenum- and tungsten-based materials. Using the diffusion Monte Carlo method, which is statistically exact for these systems, we extract binding energies of the complexes for a complete set of parameters of the model. Our results are compared with theoretical and experimental work on transition-metal dichalcogenides. Agreement is found for excitonic and trionic results, but we also observe a large discrepancy in the theoretical biexcitonic binding energies as compared to the experimental values. Possible reasons for this are outlined. Simple interpolation formulas for binding energies are provided, that can be used to easily determine the values within the accuracy of 5% for any two-dimensional semiconductor. We also calculate contact pair densities, which in the future can be used in the determination of the contact interaction.

AB - We study low-dimensional quantum systems with analytical and computational methods. Firstly, the one-dimensional extended t-V model of fermions with interactions of finite range is investigated. The model exhibits a phase transition between liquid and insulating regimes. We use various analytical approaches to generalise previous theoretical studies. We devise a strong coupling expansion to go beyond first-order perturbation theory. The method is insensitive to the presence or the lack of integrability of the system. We extract the ground state energy and critical parameters of the model near the Mott insulating commensurate density. A summary of the methods used is provided to give a broader view of their advantages and disadvantages.We also study the possible charge-density-wave phases that exist when the model is at the critical density. A complete description of phase diagrams of the model is provided: at low critical densities the phases are defined analytically, and at higher critical densities we tackle this problem computationally. We also provide a future outlook for determining the phases that occur at non-zero temperature.Secondly, we investigate Mott-Wannier complexes of two (excitons), three (trions) and four (biexcitons) charge carriers in two-dimensional semiconductors. The fermions interact through an effective interaction of a form introduced by Keldysh. Our study also includes impurity-bound complexes. We provide a classification of trions and biexcitons in transition-metal dichalcogenides, which incorporates the difference of spin polarisation between molybdenum- and tungsten-based materials. Using the diffusion Monte Carlo method, which is statistically exact for these systems, we extract binding energies of the complexes for a complete set of parameters of the model. Our results are compared with theoretical and experimental work on transition-metal dichalcogenides. Agreement is found for excitonic and trionic results, but we also observe a large discrepancy in the theoretical biexcitonic binding energies as compared to the experimental values. Possible reasons for this are outlined. Simple interpolation formulas for binding energies are provided, that can be used to easily determine the values within the accuracy of 5% for any two-dimensional semiconductor. We also calculate contact pair densities, which in the future can be used in the determination of the contact interaction.

KW - nanoscience

KW - condensed matter theory

KW - quantum Monte Carlo

KW - optoelectronics

KW - 2D semiconductors

KW - 1D quantum systems

KW - Luttinger liquid

KW - Mott insulator

KW - charge density wave

KW - excitons

KW - trions

KW - biexcitons

M3 - Doctoral Thesis

PB - Lancaster University

ER -