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A. J. Williamson

Publications and source records attributed to A. J. Williamson.

13 recordsLinked to original sources
arXiv2008

Electron Emission from Diamondoids: A Diffusion Quantum Monte Carlo Study

We present density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations designed to resolve experimental and theoretical controversies over the optical properties of H-terminated C nanoparticles (diamondoids). The QMC results follow the trends of well-converged plane-wave DFT calculations for the size dependence of the optical gap, but they predict gaps that are 1-2 eV higher. They confirm that quantum confinement effects disappear in diamondoids larger than 1 nm, which have gaps below that of bulk diamond. Our QMC calculations predict a small exciton binding energy and a negative electron affinity (NEA) for diamondoids up to 1 nm, resulting from the delocalized nature of the lowest unoccupied molecular orbital. The NEA suggests a range of possible applications of diamondoids as low-voltage electron emitters.

cond-mat.mtrl-sci↗
arXiv2005

Dielectric Response of Periodic Systems from Quantum Monte Carlo Calculations

We present a novel approach that allows to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wavefunction, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence, sampled via forward-walking. This approach has been validated for the case of an isolated hydrogen atom, and then applied to a periodic system, to calculate the dielectric susceptibility of molecular-hydrogen chains. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.

cond-mat.other↗
arXiv2004

Optimized Non-Orthogonal Localized Orbitals for Electronic Structure Calculations: Improved Linear Scaling Quantum Monte Carlo

We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of both semiconducting and metallic systems by studying bulk silicon and the homogeneous electron gas. For silicon, the improved localization of these orbitals reduces the computational time by a factor five and the memory by a factor of six compared to localized, orthogonal orbitals. For jellium, we demonstrate that the total energy is converged for orbitals truncated within spheres with radii 7-8 $r_s$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.

cond-mat.mtrl-sci↗
arXiv2001

Optical spectroscopy of single quantum dots at tunable positive, neutral and negative charge states

We report on the observation of photoluminescence from positive, neutral and negative charge states of single semiconductor quantum dots. For this purpose we designed a structure enabling optical injection of a controlled unequal number of negative electrons and positive holes into an isolated InGaAs quantum dot embedded in a GaAs matrix. Thereby, we optically produced the charge states -3, -2, -1, 0, +1 and +2. The injected carriers form confined collective 'artificial atoms and molecules' states in the quantum dot. We resolve spectrally and temporally the photoluminescence from an optically excited quantum dot and use it to identify collective states, which contain charge of one type, coupled to few charges of the other type. These states can be viewed as the artificial analog of charged atoms such as H$^{-}$, H$^{-2}$, H$^{-3}$, and charged molecules such as H$_{2}^{+}$ and H$_{3}^{+2}$. Unlike higher dimensionality systems, where negative or positive charging always results in reduction of the emission energy due to electron-hole pair recombination, in our dots, negative charging reduces the emission energy, relative to the charge-neutral case, while positive charging increases it. Pseudopotential model calculations reveal that the enhanced spatial localization of the hole-wavefunction, relative to that of the electron in these dots, is the reason for this effect.

cond-mat↗
arXiv2000

Multi-excitons in self-assembled InAs/GaAs quantum dots: A pseudopotential, many-body approach

We use a many-body, atomistic empirical pseudopotential approach to predict the multi-exciton emission spectrum of a lens shaped InAs/GaAs self-assembled quantum dot. We discuss the effects of (i) The direct Coulomb energies, including the differences of electron and hole wavefunctions, (ii) the exchange Coulomb energies and (iii) correlation energies given by a configuration interaction calculation. Emission from the groundstate of the $N$ exciton system to the $N-1$ exciton system involving $e_0\to h_0$ and $e_1\to h_1$ recombinations are discussed. A comparison with a simpler single-band, effective mass approach is presented.

cond-mat.mtrl-sci↗
arXiv2000

Theoretical interpretation of the experimental electronic structure of lens shaped, self-assembled InAs/GaAs quantum dots

We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens shaped InAs quantum dots within the ``linear combination of bulk bands'' method. We present a detailed comparison with experiment, including quantites such as the single particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole and electron hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.

cond-mat.mtrl-sci↗
arXiv1999

A pseudopotential study of electron-hole excitations in colloidal, free-standing InAs quantum dots

Excitonic spectra are calculated for free-standing, surface passivated InAs quantum dots using atomic pseudopotentials for the single-particle states and screened Coulomb interactions for the two-body terms. We present an analysis of the single particle states involved in each excitation in terms of their angular momenta and Bloch-wave parentage. We find that (i) in agreement with other pseudopotential studies of CdSe and InP quantum dots, but in contrast to k.p calculations, dot states wavefunction exhibit strong odd-even angular momentum envelope function mixing (e.g. $s$ with $p$) and large valence-conduction coupling. (ii) While the pseudopotential approach produced very good agreement with experiment for free-standing, colloidal CdSe and InP dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted spectrum does {\em not} agree well with the measured (ensemble average over dot sizes) spectra. (1) Our calculated excitonic gap is larger than the PL measure one, and (2) while the spacing between the lowest excitons is reproduced, the spacings between higher excitons is not fit well. Discrepancy (1) could result from surface states emission. As for (2), agreement is improved when account is taken of the finite size distribution in the experimental data. (iii) We find that the single particle gap scales as $R^{-1.01}$ (not $R^{-2}$), that the screened (unscreened) electron-hole Coulomb interaction scales as $R^{-1.79}$ ($R^{-0.7}$), and that the eccitonic gap sclaes as $R^{-0.9}$. These scaling laws are different from those expected from simple models.

cond-mat.mtrl-sci↗
arXiv1998

Finite size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.

cond-mat↗
arXiv1998

A Quantum Monte Carlo Approach to the Adiabatic Connection Method

We present a new method for realizing the adiabatic connection approach in density functional theory, which is based on combining accurate variational quantum Monte Carlo calculations with a constrained optimization of the ground state many-body wavefunction for different values of the Coulomb coupling constant. We use the method to study an electron gas in the presence of a cosine-wave potential. For this system we present results for the exchange-correlation hole and exchange-correlation energy density, and compare our findings with those from the local density approximation and generalized gradient approximation.

cond-mat.mtrl-sci↗
arXiv1998

Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon

The band structure of silicon is calculated at the Gamma, X, and L wave vectors using diffusion quantum Monte Carlo methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low lying excitations in solids.

cond-mat↗
arXiv1998

Prediction of a Strain Induced Conduction Band Minimum in Embedded Quantum Dots

Free standing InP quantum dots have previously been theoretically and experimentally shown to have a direct band gap across a large range of experimentally accessible sizes. We demonstrate that when these dots are embedded coherently within a GaP barrier material, the effects of quantum confinement in conjunction with coherent strain suggest there will be a critical diameter of dot (60A), above which the dot is direct, type I, and below which it is indirect, type II. However, the strain in the system acts to produce another conduction state with an even lower energy, in which electrons are localized in small pockets at the interface between the InP dot and the GaP barrier. Since this conduction state is GaP X_1c-derived and the highest occupied valence state is InP, Gamma-derived, the fundamental transition is predicted to be indirect in both real and reciprocal space (``type II'') for all dot sizes. This effect is peculiar to the strained dot, and is absent in the free-standing dot.

cond-mat.mtrl-sci↗
arXiv1997

Comparison of two methods for describing the strain profiles in quantum dots

The electronic structure of interfaces between lattice-mismatched semiconductor is sensitive to the strain. We compare two approaches for calculating such inhomogeneous strain -- continuum elasticity (CE, treated as a finite difference problem) and atomistic elasticity (AE). While for small strain the two methods must agree, for the large strains that exist between lattice-mismatched III-V semiconductors (e.g. 7% for InAs/GaAs outside the linearity regime of CE) there are discrepancies. We compare the strain profile obtained by both approaches (including the approximation of the correct C_2 symmetry by the C_4 symmetry in the CE method), when applied to C_2-symmetric InAs pyramidal dots capped by GaAs.

cond-mat.mtrl-sci↗