Thesis--University of Colorado. / Bibliography: p. 179-182.

The work in this thesis is concerned with the application and development of quantum Monte Carlo (QMC) methods. We begin by proposing a technique to maximise the efficiency of the extrapolation of DMC results to zero time step, finding that a relative time step ratio of 1:4 is optimal. We discuss the post-processing of QMC data and the calculation of accurate error bars by reblocking, setting out criteria for the choice of block length. We then quantify the effects of uncertainty in the correlation length on estimated error bars, finding that the frequency of outliers is significantly increased for short runs. We then report QMC calculations of biexciton binding energies in bilayer systems. We have also calculated exciton-exciton interaction potentials, and radial distribution functions for electrons and holes in bound biexcitons. We find a larger region of biexciton stability than other recent work [C. Schindler and R. Zimmermann, Phys. Rev. B 78,045313 (2008)]. We also find that individual excitons retain their identity in bound biexcitons for large layer separations. Finally, we give details of a QMC study of the one-dimensional homogeneous electrongas (1D HEG). We present calculations of the energy, pair correlation function, static structure factor (SSF), and momentum density (MD) for the 1D HEG. We observe peaks in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around the Fermi wave vector, finding good agreement between the exponents of the ferromagnetic infinitely-thin and harmonic wires.

For nearly a decade, quasi-one-dimensional conductors have been the subject of intensive study. Theoretically, much attention has been devoted to the development of one-dimensional Fermi gas models, some which may be solved exactly, and to the calculation of their response functions. After a review of this theory, a different approach is adopted in the investigation of two models. The dielectric response theory of the three-dimensional Coulomb gas has been applied to an anisotropic system in which the particles interact with an effective one-dimensional long-range potential. Within the framework of the approximation of Singwi, Tosi, Land, and Sjolander, the dielectric properties of the model are examined in order to determine the conditions under which it is unstable with respect to formation of a charge density wave state. It is found that the positive neutralizing background must be polarizable in order for such an instability to occur. The same approximation method, when applied to a one-dimensional fermion gas with a ʃ-function interaction may be compared with the exact solution of Yang. This solution, which exists in the form of coupled integral equations, has been calculated numerically, and, as predicted by the Lieb-Mattis theorem, the ground state is found to be non-magnetic. The approximation of Singwi et al. proves to give better correlation energies than other inexact methods, particularly at higher densities. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Oxide heterostructures are attracting huge interest in recent years due to the special functionalities of quasi two-dimensional quantum gases. In this thesis, the electronic states at the interface between perovskite oxides and pyrite compounds have been studied by first-principles calculations based on density functional theory. Optimization of the atomic positions are taken into account, which is considered very important at interfaces, as observed in the case of LaAlO3/SrTiO3. The creation of metallic states at the interfaces thus is explained in terms of charge transfer between the transition metal and oxygen atoms near the interface. It is observed that with typical thicknesses of at least 10-12 °A the gases still extend considerably in the third dimension, which essentially determines the magnitude of quantum mechanical effects. To overcome this problem, we propose incorporation of highly electronegative cations (such as Ag) in the oxides. A fundamental interest is also the thermodynamic stability of the interfaces due to the possibility of atomic intermixing in the interface region. Therefore, different cation intermixed configurations are taken into account for the interfaces aiming at the energetically stable state. The effect of O vacancies is also discussed for both polar and non-polar heterostructures. The interface metallicity is enhanced for the polar system with the creation of O vacancies, while the clean interface at the non-polar heterostructure exhibits an insulating state and becomes metallic in presence of O vacancy. The O vacancy formation energies are calculated and explained in terms of the increasing electronegativity and effective volume of A the side cation. Along with these, the electronic and magnetic properties of an interface between the ferromagnetic metal CoS2 and the non-magnetic semiconductor FeS2 is investigated. We find that this contact shows a metallic character. The CoS2 stays quasi half metallic at the interface, while the FeS2 becomes metallic. At the interface, ferromagnetic ordering is found to be energetically favorable as compared to antiferromagnetic ordering. Furthermore, tensile strain is shown to strongly enhance the spin polarization so that a virtually half-metallic interface can be achieved, for comparably moderate strain. Our detailed study is aimed at complementing experiments on various oxide interfaces and obtaining a general picture how factors like cations, anions, their atomic weights and elecronegativities, O vacancies, lattice mismatch, lattice relaxation, magnetism etc play a combined role in device design.

<p> It is known in the case of an electron gas that the Coulomb force between electrons is screened due to the density variation around the electrons. In a similar way the force acting between nucleons in nuclear matter may be appreciably different from the free nucleon-nucleon interactions. The main theme of this thesis is to examine the "Screening" effect of the nuclear force. To this end, first the dielectric formulation of the theory of an electron gas is reviewed. Relationship among the chain-diagram approximation, the random phase approximation and the dieledtric formulation is discussed in detail. These techniques are then applied to nuclear matter taking the one-pion exchange potential as an example. It is found that the screening effect on the nuclear force in nuclear matter is indeed quite appreciable. The validity of the approximations is discussed. </p> / Thesis / Master of Science (MSc)

This thesis describes the application of coupled-cluster theory to model systems of metallic solids and cold-atom gases. First, I give an overview of both ground- and excited-state coupled cluster theory as background for the main topics in this thesis. Next, I evaluate the accuracy of several cost-saving approaches in estimating the coupled cluster correlation energy for a model metallic system, the uniform electron gas, in the complete basis set and thermodynamic limits. After that, I present calculations of the spectral function of the uniform electron gas in these same limits, the results of which are rationalized by applying a bosonized coupled-cluster theory to an approximate, simplified Hamiltonian that couples plasmons to a structureless core hole state. Finally, I show how coupled-cluster theory captures the many-body nature of two-component Fermi gases with tunable, attractive interactions.

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We have studied the electronic properties of AlxGa1-xN/GaN heterostructures by using Shubnikov¡Vde Haas(SdH) measurement. Two SdH oscillations were detected on the samples of x=0.35 and 0.31, due to the population of the first two subbands with the energy separations of 128 and 109 meV, respectively. For the sample of x=0.25, two SdH oscillations beat each other, probably due to a finite zero-field spin splitting. The spin-splitting energy is equal to 9.0 meV. The samples also showed a persistent photoconductivity effect after illuminating by blue light-emitting diode. For the part of experiment , we installed a "Regulator" on low temperature and high magnetic field system, in order to control the temperature of sample from 0.3K to 10K accurately. For the convenience of SdH measurements at different tempertures.