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A one-dimensional quantum wire of Fermions is considered and ground state properties are calculated in the high density regime within the extended quasiparticle picture and Born approximation. Expanding the two-particle Green functions determines the selfenergy and the polarization as well as the response function on the same footing. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behaviour shows a rich structure of a gap in the damping of excitation which is closed when the momentum approaches the Fermi one. The consistent spectral function is presented completing the first two energy-weighted sum rules. The excitation spectrum shows a splitting due to holons and antiholons as non-Fermi liquid behaviour. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield shows a dip as onset of Peierls instability. The correlation energy is calculated with the help of the extended quasiparticle picture which accounts for off-shell effects. The corresponding response function leads to the same correlation energy as the selfenergy in agreement with perturbation theory. The reduced density matrix or momentum distribution is calculated with the help of a Pad\'e regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behaviour is repaired in this way., Comment: In memory of Paul Ziesche (1933-2022)

The selfenergy in Born approximation including exchange of interacting one-dimensional systems is expressed in terms of a single integral about the potential which allows a fast and precise calculation for any potential analytically. The imaginary part of the self energy as damping of single-particle excitations shows a rich structure of different areas limited by single-particle and collective excitation lines. The corresponding spectral function reveals a pseudogap, a splitting of excitation into holons and antiholons as well as bound states.

Positron annihilation in solid state matter can be utilized to detect and identify open-volume defects. The momentum distribution of the annihilation radiation is an important observable in positron-based measurements, and can reveal information on the chemical surroundings of the defect sites. In this work we present a variational quantum Monte Carlo method for simulation of the momentum densities of annihilating electron-positron pairs in semiconductors and insulators. We study finite-size effects, effects of lattice vibrations, and different levels of trial wave functions. Small simulation cells and simple wave function forms are found to be sufficient for accurate calculations in simulation of pristine lattices, enabling cheap accumulation of results. We compare calculated predictions of the Doppler broadening of the 511-keV 2{\gamma} annihilation line of the in aluminium nitride and silicon against experimental data measured from reference samples. Our results achieve better agreement with experiments in the these materials than conventional state-of-the-art methods, and proves that direct modeling of the electron-positron correlations is important for a supporting theory of positron annihilation sprectroscopies, Comment: 10 pages, 4 figures

Recent advances in fabrication of two dimensional materials and their moir\'e heterostructures have opened up new avenues for realization of ground-state excitonic insulators, where the structure spontaneously develops a finite interlayer electronic polarization. We propose and analyze a scheme where an optically generated intralayer exciton is screened by excitations out of the excitonic insulator to form interlayer polarons. Using Quantum Monte-Carlo calculations we first determine the binding energy of the biexciton state composed of inter- and intralayer excitons, which plays a central role in understanding polaron formation. We describe the excitations out of the ground-state condensate using BCS theory and use a single interacting-quasiparticle-pair excitation Ansatz to describe dynamical screening of optical excitations. Our predictions carry the hallmarks of the excitonic insulator excitation spectrum and show how changing the interlayer exciton binding energy by increasing the layer separation modifies the optical spectra.

We describe how the out-of-plane dielectric polarizability of monolayer graphene influences the electrostatics of bilayer graphene -- both Bernal (BLG) and twisted (tBLG). We compare the polarizability value computed using density functional theory with the output from previously published experimental data on the electrostatically controlled interlayer asymmetry potential in BLG and data on the on-layer density distribution in tBLG. We show that monolayers in tBLG are described well by polarizability $\alpha_{exp} = 10.8 \unicode{x212B}^3$ and effective out-of-plane dielectric susceptibility $\epsilon_z = 2.5$, including their on-layer electron density distribution at zero magnetic field and the inter-layer Landau level pinning at quantizing magnetic fields., Comment: 4 pages

Due to their unique two-dimensional nature, charge carriers in semiconducting transition metal dichalcogenides (TMDs) exhibit strong unscreened Coulomb interactions and sensitivity to defects and impurities. The versatility of van der Waals layer stacking allows spatially separating electrons and holes between different TMD layers with staggered band structure, yielding interlayer few-body excitonic complexes whose nature is still debated. Here we combine quantum Monte Carlo calculations with spectrally and temporally resolved photoluminescence measurements on a top- and bottom-gated MoSe2/WSe2 heterostructure, and identify the emitters as impurity-bound interlayer excitonic complexes. Using independent electrostatic control of doping and out-of-plane electric field, we demonstrate control of the relative populations of neutral and charged complexes, their emission energies on a scale larger than their linewidth, and an increase of their lifetime into the microsecond regime. This work unveils new physics of confined carriers and is key to the development of novel optoelectronics applications.

Excitonic complexes in type-II quantum-ring heterostructures may be considered as artificial atoms due to the confinement of only one charge-carrier type in an artificial nucleus. Binding energies of excitons, trions, and biexcitons in these nanostructures are then effectively ionization energies of these artificial atoms. The binding energies reported here are calculated within the effective-mass approximation using the diffusion quantum Monte Carlo method and realistic geometries for gallium antimonide rings in gallium arsenide. The electrons form a halo outside the ring, with very little charge density inside the central cavity of the ring. The de-excitonization and binding energies of the complexes are relatively independent of the precise shape of the ring.

We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC methods on atoms, molecules, and solids. We propose a finite-size-error correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We show that finite-size effects are qualitatively different in two-dimensional materials, demonstrating the effect in a QMC calculation of the band gap and exciton binding energy of monolayer phosphorene. We investigate the fixed-node errors in diffusion Monte Carlo gaps evaluated with Slater-Jastrow trial wave functions by examining the effects of backflow transformations, and also by considering the formation of restricted multideterminant expansions for excited-state wave functions. For several molecules, we examine the importance of structural relaxation in the excited state in determining excited-state energies. We study the feasibility of using variational Monte Carlo with backflow correlations to obtain accurate excited-state energies at reduced computational cost, finding that this approach can be valid. We find that diffusion Monte Carlo gap calculations can be performed with much larger time steps than are typically required to converge the total energy, at significantly diminished computational expense, but that in order to alleviate fixed-node errors in calculations on solids the inclusion of backflow correlations is sometimes necessary., Comment: 24 pages, including 11 figures

A new phase V of hydrogen was recently claimed in experiments above 325 GPa and 300 K. Due to the extremely small sample size at such record pressures the measurements were limited to Raman spectroscopy. The experimental data on increase of pressure shows decreasing Raman activity and darkening of the sample, which suggests band-gap closure and impending molecular dissociation, but no definite conclusions could be reached. Furthermore, the available data is insufficient to determine the structure of phase V, which remains unknown. Introducing saddle-point $ab$ $initio$ random structure searching (sp-AIRSS), we find several new structural candidates of hydrogen which could describe the observed properties of phase V. We investigate hydrogen metallisation in the proposed candidate structures, and demonstrate that smaller band gaps are associated with longer bond lengths. We conclude that phase V is a stepping stone towards metallisation., Comment: 7 pages, 3 figures, includes Supplemental Material

We present theoretical results for the radiative rates and doping-dependent photoluminescence spectrum of interlayer excitonic complexes localized by donor impurities in MoSe$_2$/WSe$_2$ twisted heterobilayers, supported by quantum Monte Carlo calculations of binding energies and wave-function overlap integrals. For closely aligned layers, radiative decay is made possible by the momentum spread of the localized complexes' wave functions, resulting in few $\mu$s$^{-1}$ radiative rates. For strongly misaligned layers, the short-range interaction between the carriers and impurity provides a finite radiative rate with a strong asymptotic twist angle dependence $\propto \theta^{-8}$. Finally, phonon-assisted recombination is considered, with emission of optical phonons in both layers resulting in additional weaker emission lines, redshifted by the phonon energy., Comment: 19 pages, including 11 figures and 5 appendices

We predict a fast relaxation of photo-excited carriers in monolayer transition metal dichalcogenides (TMDCs), which is mediated by the emission of longitudinal optical (LO) phonons. By evaluating Born effective charges for ${\rm MoS_2, MoSe_2,WS_2}$, and ${\rm WSe_2}$, we find that, due to the polar coupling of electrons with LO phonons, the relaxation times for hot electrons and holes are of the order of a few ps., Comment: 4 pages, 3 figures

We present $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians parametrised by {\it ab initio} density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the $K$, $Q$, $\Gamma$, and $M$ points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides. We review the parametrisation of the essential parts of the $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians for MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, including the spin-splitting and spin-polarisation of the bands, and we discuss the vibrational properties of these materials. We then use $\mathbf{k}\cdotp\mathbf{p}$ theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the $M$ points). We also discuss the visualisation of scanning tunnelling microscopy maps., Comment: topical review, 52 pages, 16 MB. The arXiv version contains a couple of more relevant experimental references, which have appeared very recently, than the published version

We map the three-body problem in two dimensions onto one particle in a three dimensional potential treatable by a purposely-developed boundary-matching-matrix method. We evaluate binding energies of trions $X^{\pm}$, excitons bound by a donor/acceptor charge $X^{D/A}$, and overcharged acceptors/donors in two-dimensional atomic crystals of transition metal dichalcogenides, where interaction between charges features logarithmic behavior at intermediate distances. We find that dissociation energy of $X^{\pm}$ is, typically, much larger than that of localised exciton complexes, so that trions are more resilient to heating, despite that their recombination line in optics is much less red-shifted from the exciton line, as compared to $X^{D/A}$, Comment: 5.1 pages, 3 figures,+ supplementary material (5 pages); Improved numerics; Monte Carlo data added; Published version

We derive an effective Hamiltonian which describes the dynamics of electrons in the conduction band of transition metal dichalcogenides (TMDC) in the presence of perpendicular electric and magnetic fields. We discuss in detail both the intrinsic and the Bychkov-Rashba spin-orbit coupling (SOC) induced by an external electric field. We point out interesting differences in the spin-split conduction band between different TMDC compounds. An important consequence of the strong intrinsic SOC is an effective out-of-plane $g$-factor for the electrons which differs from the free-electron g-factor $g\simeq 2$. We identify a new term in the Hamiltonian of the Bychkov-Rashba SOC which does not exist in III-V semiconductors. Using first-principles calculations, we give estimates of the various parameters appearing in the theory. Finally, we consider quantum dots (QDs) formed in TMDC materials and derive an effective Hamiltonian which allows us to calculate the magnetic field dependence of the bound states in the QDs. We find that all states are both valley and spin split, which suggests that these QDs could be used as valley-spin filters. We explore the possibility of using spin and valley states in TMDCs as quantum bits, and conclude that, due to the relatively strong intrinsic spin-orbit splitting in the conduction band, the most realistic option appears to be a combined spin-valley (Kramers) qubit at low magnetic fields., Comment: minor corrections made

The non-additive dispersion contribution to the binding energy of three one-dimensional (1D) wires is investigated using wires modelled by (i) chains of hydrogen atoms and (ii) homogeneous electron gases. We demonstrate that the non-additive dispersion contribution to the binding energy is significantly enhanced compared with that expected from Axilrod-Teller-Muto-type triple-dipole summations and follows a different power-law decay with separation. The triwire non-additive dispersion for 1D electron gases scales according to the power law $d^{-\beta}$, where $d$ is the wire separation, with exponents $\beta(r_s)$ smaller than 3 and slightly increasing with $r_s$ from 2.4 at $r_s = 1$ to 2.9 at $r_s=10$, where $r_s$ is the density parameter of the 1D electron gas. This is in good agreement with the exponent $\beta=3$ suggested by the leading-order charge-flow contribution to the triwire non-additivity, and is a significantly slower decay than the $\sim d^{-7}$ behaviour that would be expected from triple-dipole summations., Comment: 10 pages, 8 figures, 1 table