arXiv subjects

N. D. Drummond

Publications and source records attributed to N. D. Drummond.

At least 55 records · Page 3Linked to original sources

arXiv2013

Quantum Monte Carlo calculation of the Fermi liquid parameters of the two-dimensional homogeneous electron gas

Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of "best available" values for the Fermi liquid parameters.

cond-mat.quant-gas↗

arXiv2013

Band Structure and Optical Transitions in Atomic Layers of Hexagonal Gallium Chalcogenides

We report density-functional-theory calculations of the electronic band structures and optical absorption spectra of two-dimensional crystals of Ga$_2$X$_2$ (X=S, Se, and Te). Our calculations show that all three two-dimensional materials are dynamically stable indirect-band-gap semiconductors with a Mexican-hat dispersion of holes near the top of the valence band. We predict the existence of Lifshitz transitions---changes in the Fermi-surface topology of hole-doped Ga$_2$X$_2$---at hole concentrations $n_{S}=7.96\times 10^{13}$ cm$^{-2}$, $n_{Se}=6.13\times 10^{13}$ cm$^{-2}$, and $n_{Te}=3.54\times 10^{13}$ cm$^{-2}$.

cond-mat.mes-hall↗

arXiv2013

Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress

A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at finite temperatures. The low-energy portion of the Born-Oppenheimer energy surface is mapped and used to calculate the total vibrational energy including anharmonic effects, electron-phonon coupling, and the vibrational contribution to the stress tensor. We report results for the temperature dependence of the electronic band gap and the linear coefficient of thermal expansion of diamond, lithium hydride, and lithium deuteride.

cond-mat.mtrl-sci↗

arXiv2012

Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas

The quasiparticle effective mass is a key quantity in the physics of electron gases, describing the renormalization of the electron mass due to electron-electron interactions. Two-dimensional electron gases are of fundamental importance in semiconductor physics, and there have been numerous experimental and theoretical attempts to determine the quasiparticle effective mass in these systems. In this work we report quantum Monte Carlo results for the quasiparticle effective mass of a two-dimensional homogeneous electron gas. Our calculations differ from previous quantum Monte Carlo work in that much smaller statistical error bars have been achieved, allowing for an improved treatment of finite-size effects. In some cases we have also been able to use larger system sizes than previous calculations.

cond-mat.quant-gas↗

arXiv2012

Electrically Tunable Band Gap in Silicene

We report calculations of the electronic structure of silicene and the stability of its weakly buckled honeycomb lattice in an external electric field oriented perpendicular to the monolayer of Si atoms. We find that the electric field produces a tunable band gap in the Dirac-type electronic spectrum, the gap being suppressed by a factor of about eight by the high polarizability of the system. At low electric fields, the interplay between this tunable band gap, which is specific to electrons on a honeycomb lattice, and the Kane-Mele spin-orbit coupling induces a transition from a topological to a band insulator, whereas at much higher electric fields silicene becomes a semimetal.

cond-mat.mes-hall↗

arXiv2012

Strategies for improving the efficiency of quantum Monte Carlo calculations

We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte Carlo method. Our finding that a relative time-step ratio of 1:4 is optimal in DMC is in agreement with the result of [J. Vrbik and S.M.Rothstein, Intern. J. Quantum Chem. 29, 461-468 (1986)]. Finally, we discuss the removal of serial correlation from data sets by reblocking, setting out criteria for the choice of block length and quantifying the effects of the uncertainty in the estimated correlation length.

physics.comp-ph↗

arXiv2011

Quantum Monte Carlo, time-dependent density functional theory, and density functional theory calculations of diamondoid excitation energies and Stokes shifts

We have computed the absorption and emission energies and hence Stokes shifts of small diamondoids as a function of size using different theoretical approaches, including density functional theory and quantum Monte Carlo (QMC) calculations. The absorption spectra of these molecules were also investigated by time-dependent density functional theory (TD-DFT) and compared with experiment. We have analyzed the structural distortion and formation of a self-trapped exciton in the excited state, and we have studied the effects of these on the Stokes shift as a function of size. Compared to recent experiments, QMC overestimates the excitation energies by about 0.8(1) eV on average. Benefiting from a cancellation of errors, the optical gaps obtained in DFT calculations with the B3LYP functional are in better agreement with experiment. It is also shown that TD-B3LYP calculations can reproduce most of the features found in the experimental spectra. According to our calculations, the structures of diamondoids in the excited state show a distortion which is hardly noticeable compared to that found for methane. As the number of diamond cages is increased, the distortion mechanism abruptly changes character. We have shown that the Stokes shift is size-dependent and decreases with the number of diamond cages. The rate of decrease in the Stokes shift is on average 0.1 eV per cage for small diamondoids.

physics.atm-clus↗

arXiv2011

Quantum Monte Carlo Study of a Positron in an Electron Gas

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects.

cond-mat.stat-mech↗

arXiv2011

Ground state properties of the one-dimensional electron liquid

We present calculations of the energy, pair correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve 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 exponent of the ferromagnetic infinitely-thin wire and the ferromagnetic harmonic wire.

cond-mat.str-el↗

arXiv2011

Quantum Monte Carlo calculation of the zero-temperature phase diagram of the two-component fermionic hard-core gas in two dimensions

Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram, by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range r^(-3) potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.

cond-mat.quant-gas↗

arXiv2010

Diamond -> beta-tin phase transition in Si within diffusion quantum Monte Carlo

We have studied the diamond -> beta-tin phase transition in Si using diffusion quantum Monte Carlo (DMC) methods. Slater-Jastrow-backflow trial wave functions give lower DMC energies than Slater-Jastrow ones, and backflow slightly favors the beta-tin phase with respect to the diamond phase. We have investigated the changes in the equation of state that result from the use of different pseudopotentials, the inclusion of either zero-point motion or finite-temperature vibrations, and the application of corrections for finite-size effects. Our tests indicate that the choice of pseudopotential can significantly affect the equation of state. Using a Dirac-Fock pseudopotential leads to an overestimation of the transition pressure but an empirical pseudopotential designed for use in correlated calculations gives a transition pressure in quite good agreement with experiment.

cond-mat.mtrl-sci↗

arXiv2010

Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %.

cond-mat.mtrl-sci↗

arXiv2010

First-Principles Study of a Positron Immersed in an Electron Gas

Calculations of the relaxation energy, contact pair-correlation function, and annihilating-pair momentum density for a single positron immersed in a homogeneous electron gas are presented. We achieve an accurate description of the electron-positron correlation effects by working in the reference frame in which the positron is stationary and using a mean-field approach based on single-component density functional theory. Our positron relaxation energies and annihilation rates are similar to those from the best existing many-body calculations. Our annihilating-pair momentum densities are significantly different from previous data, and include a "tail" beyond the Fermi edge.

cond-mat.mes-hall↗

arXiv2010

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

cond-mat.mtrl-sci↗

arXiv2010

Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair correlation function, static structure factor, and momentum density of the ground state of the two-dimensional homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

cond-mat.mes-hall↗

arXiv2010

Quantum Monte Carlo calculation of the energy band and quasiparticle effective mass of the two-dimensional Fermi fluid

We have used the diffusion quantum Monte Carlo method to calculate the energy band of the two-dimensional homogeneous electron gas (HEG), and hence we have obtained the quasiparticle effective mass and the occupied bandwidth. We find that the effective mass in the paramagnetic HEG increases significantly when the density is lowered, whereas it decreases in the fully ferromagnetic HEG. Our calculations therefore support the conclusions of recent experimental studies [Y.-W. Tan et al., Phys. Rev. Lett. 94, 016405 (2005); M. Padmanabhan et al., Phys. Rev. Lett. 101, 026402 (2008); T. Gokmen et al., Phys. Rev. B 79, 195311 (2009)]. We compare our calculated effective masses with other theoretical results and experimental measurements in the literature.

cond-mat.mes-hall↗

arXiv2010

Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas

We have used quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter r_s=31(1) a.u. and a transition to a ferromagnetic crystal at r_s=38(5) a.u. The fully spin-polarized fluid is never stable. We searched for, but did not find, the ferromagnetic hybrid phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)].

cond-mat.mes-hall↗

arXiv2008

Exciton-exciton interaction and biexciton formation in bilayer systems

We report quantum Monte Carlo calculations of biexciton binding energies in ideal two-dimensional bilayer systems with isotropic electron and hole masses. We have also calculated exciton-exciton interaction potentials, and pair distribution functions for electrons and holes in bound biexcitons. Comparing our data with results obtained in a recent study using a model exciton-exciton potential [C. Schindler and R. Zimmermann, Phys. Rev. B \textbf{78}, 045313 (2008)], we find a somewhat larger range of layer separations at which biexcitons are stable. We find that individual excitons retain their identity in bound biexcitons for large layer separations.

cond-mat.str-el↗