Diffusion quantum Monte Carlo and GW study of the electronic properties of monolayer and bulk hexagonal boron nitride

© 2020 American Physical Society. We report diffusion quantum Monte Carlo (DMC) and many-body GW calculations of the electronic band gaps of monolayer and bulk hexagonal boron nitride (hBN). We find the monolayer band gap to be indirect. GW predicts much smaller quasiparticle gaps at both the single-shot G0W0 and the partially self-consistent GW0 levels. In contrast, solving the Bethe-Salpeter equation on top of the GW0 calculation yields an exciton binding energy for the direct exciton at the K point in close agreement with the DMC value. Vibrational renormalization of the electronic band gap is found to be significant in both the monolayer and the bulk. Taking vibrational effects into account, DMC overestimates the band gap of bulk hBN, while GW theory underestimates it

Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo binding-energy data for Mott-Wannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using first-order perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the in-plane polarizability.</p

Discovering quantum phase transitions with fermionic neural networks

Deep neural networks have been extremely successful as highly accurate wave function ans\"atze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network is given no \emph{a priori} knowledge that a phase transition exists, but converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density

Diffusion quantum Monte Carlo study of excitonic complexes in two-dimensional transition-metal dichalcogenides

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide (i) statistically exact diffusion quantum Monte Carlo binding-energy data for a Mott-Wannier model of (donor/acceptor-bound) excitons, trions, and biexcitons in two-dimensional semiconductors in which charges interact via the Keldysh potential, (ii) contact pair-distribution functions to allow a perturbative description of contact interactions between charge carriers, and (iii) an analysis and classification of the different types of bright trions and biexcitons that can be seen in single-layer molybdenum and tungsten dichalcogenides. We investigate the stability of biexcitons in which two charge carriers are indistinguishable, finding that they are only bound when the indistinguishable particles are several times heavier than the distinguishable ones. Donor/acceptor-bound biexcitons have similar binding energies to the experimentally measured biexciton binding energies. We predict the relative positions of all stable free and bound excitonic complexes of distinguishable charge carriers in the photoluminescence spectra of WSe2 and MoSe2

Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures.

Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead, our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is non-metallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.We thank Dominik Jochym for help with the implementation of the BLYP density functional. Financial support was provided by the Engineering and Physical Sciences Research Council (EPSRC), U.K. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. Additional calculations were performed on the Cambridge High Performance Computing Service facility Darwin and the N8 high-performance computing facility provided and funded by the N8 consortium and EPSRC (Grant No. EP/K000225/1). We thank Dominik Jochym for help with the mplementation of the BLYP density functional. Financial support was provided by the Engineering and Physical Sciences Research Council (EPSRC), U.K. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. Additional calculations were performed on the Cambridge High Performance Computing Service facility Darwin and the N8 high-performance computing facility provided and funded by the N8 consortium and EPSRC (Grant No. EP/K000225/1).This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/ncomms879

Graviton Propagation and Vacuum Polarization in Curved Space

The effects of vacuum polarization arising from loops of massive scalar particles on graviton propagation in curved space are considered. Physically, they are due to curvature induced tidal forces acting on the cloud of virtual scalar particles surrounding the graviton. The effects are tractable in a WKB and large mass limit and the results can be written as an effective refractive index for the graviton modes with both a real and imaginary part. The imaginary part of the refractive index is a curvature induced contribution to the wavefunction renormalization of the graviton in real affine time and can have the effect of dressing or un-dressing the graviton. The real part of the refractive index increases logarithmically at high frequency as long as the null energy condition is satisfied by the background.Comment: 21 pages, typos correcte

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table

Spatially-resolved electronic and vibronic properties of single diamondoid molecules

Diamondoids are a unique form of carbon nanostructure best described as hydrogen-terminated diamond molecules. Their diamond-cage structures and tetrahedral sp3 hybrid bonding create new possibilities for tuning electronic band gaps, optical properties, thermal transport, and mechanical strength at the nanoscale. The recently-discovered higher diamondoids (each containing more than three diamond cells) have thus generated much excitement in regards to their potential versatility as nanoscale devices. Despite this excitement, however, very little is known about the properties of isolated diamondoids on metal surfaces, a very relevant system for molecular electronics. Here we report the first molecular scale study of individual tetramantane diamondoids on Au(111) using scanning tunneling microscopy and spectroscopy. We find that both the diamondoid electronic structure and electron-vibrational coupling exhibit unique spatial distributions characterized by pronounced line nodes across the molecular surfaces. Ab-initio pseudopotential density functional calculations reveal that the observed dominant electronic and vibronic properties of diamondoids are determined by surface hydrogen terminations, a feature having important implications for designing diamondoid-based molecular devices.Comment: 16 pages, 4 figures. to appear in Nature Material

Genomic epidemiology reveals transmission patterns and dynamics of SARS-CoV-2 in Aotearoa New Zealand

New Zealand, a geographically remote Pacific island with easily sealable borders, implemented a nationwide 'lockdown' of all non-essential services to curb the spread of COVID-19. Here, we generate 649 SARS-CoV-2 genome sequences from infected patients in New Zealand with samples collected during the 'first wave', representing 56% of all confirmed cases in this time period. Despite its remoteness, the viruses imported into New Zealand represented nearly all of the genomic diversity sequenced from the global virus population. These data helped to quantify the effectiveness of public health interventions. For example, the effective reproductive number, Re of New Zealand's largest cluster decreased from 7 to 0.2 within the first week of lockdown. Similarly, only 19% of virus introductions into New Zealand resulted in ongoing transmission of more than one additional case. Overall, these results demonstrate the utility of genomic pathogen surveillance to inform public health and disease mitigation

Why Is the Correlation between Gene Importance and Gene Evolutionary Rate So Weak?

One of the few commonly believed principles of molecular evolution is that functionally more important genes (or DNA sequences) evolve more slowly than less important ones. This principle is widely used by molecular biologists in daily practice. However, recent genomic analysis of a diverse array of organisms found only weak, negative correlations between the evolutionary rate of a gene and its functional importance, typically measured under a single benign lab condition. A frequently suggested cause of the above finding is that gene importance determined in the lab differs from that in an organism's natural environment. Here, we test this hypothesis in yeast using gene importance values experimentally determined in 418 lab conditions or computationally predicted for 10,000 nutritional conditions. In no single condition or combination of conditions did we find a much stronger negative correlation, which is explainable by our subsequent finding that always-essential (enzyme) genes do not evolve significantly more slowly than sometimes-essential or always-nonessential ones. Furthermore, we verified that functional density, approximated by the fraction of amino acid sites within protein domains, is uncorrelated with gene importance. Thus, neither the lab-nature mismatch nor a potentially biased among-gene distribution of functional density explains the observed weakness of the correlation between gene importance and evolutionary rate. We conclude that the weakness is factual, rather than artifactual. In addition to being weakened by population genetic reasons, the correlation is likely to have been further weakened by the presence of multiple nontrivial rate determinants that are independent from gene importance. These findings notwithstanding, we show that the principle of slower evolution of more important genes does have some predictive power when genes with vastly different evolutionary rates are compared, explaining why the principle can be practically useful despite the weakness of the correlation