Metallization of solid molecular hydrogen in two dimensions: Mott-Hubbard-type transition

We analyze the pressure-induced metal-insulator transition in a two-dimensional vertical stack of $H_2$ molecules in x-y plane, and show that it represents a striking example of the Mott-Hubbard-type transition. Our combined exact diagonalization approach, formulated and solved in the second quantization formalism, includes also simultaneous ab initio readjustment of the single-particle wave functions, contained in the model microscopic parameters. The system is studied as a function of applied side force (generalized pressure), both in the $H_2$-molecular and $H$-quasiatomic states. Extended Hubbard model is taken at the start, together with longer-range electron-electron interactions incorporated into the scheme. The stacked molecular plane transforms discontinuously into a (quasi)atomic state under the applied force via a two-step transition: the first between molecular insulating phases and the second from the molecular to the quasiatomic metallic phase. No quasiatomic insulating phase occurs. All the transitions are accompanied by an abrupt changes of the bond length and the intermolecular distance (lattice parameter), as well as by discontinuous changes of the principal electronic properties, which are characteristic of the Mott-Hubbard transition here associated with the jumps of the predetermined equilibrium lattice parameter and the effective bond length. The phase transition can be interpreted in terms of the solid hydrogen metallization under pressure exerted by e.g., the substrate covered with a monomolecular $H_2$ film of the vertically stacked molecules. Both the Mott and Hubbard criteria at the insulator to metal transition are discussed

Discontinuous transition of molecular-hydrogen chain to the quasi-atomic state: Exact diagonalization - ab initio approach

We obtain in a direct and rigorous manner a transition from a stable molecular hydrogen $nH_2$ single chain to the quasiatomic two-chain $2nH$ state. We devise an original method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double-counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains possible to tackle, $n=3\div6$. The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio $U/W$ reflects the Mott--Hubbard-transition aspect of the atomization. Universal feature of the transition relation to the Mott criterion for the insulator--metal transition is also noted. The role of the electron correlations is thus shown to be of fundamental significance.Comment: 6 pages, 5 figures, 1 tabl

Combined shared and distributed memory ab-initio computations of molecular-hydrogen systems in the correlated state: process pool solution and two-level parallelism

An efficient computational scheme devised for investigations of ground state properties of the electronically correlated systems is presented. As an example, $(H_{2})_{n}$ chain is considered with the long-range electron-electron interactions taken into account. The implemented procedure covers: (i) single-particle Wannier wave-function basis construction in the correlated state, (ii) microscopic parameters calculation, and (iii) ground state energy optimization. The optimization loop is based on highly effective process-pool solution - specific root-workers approach. The hierarchical, two-level parallelism was applied: both shared (by use of Open Multi-Processing) and distributed (by use of Message Passing Interface) memory models were utilized. We discuss in detail the feature that such approach results in a substantial increase of the calculation speed reaching factor of $300$ for the fully parallelized solution.Comment: 14 pages, 10 figures, 1 tabl

Kinetyka uporządkowania i termodynamika wakancji termicznych w układach międzymetalicznych z nadstrukturą typu B2 : badania symulacyjne

Celem niniejszej pracy jest opracowanie modelu kinetyki porządkowania atomowego w związkach międzymetalicznych z nadstrukturą typu B2 metodami symulacji komputerowych opartych na technikach Monte Carlo. Do grupy badanych związków metalicznych należą min. NiAl, FeAl, które ze względu na niską gęstość i wysoką odporność na działanie wysokich temperatur są kandydatami do zastosowań w nowoczesnej technologii materiałów konstrukcyjnych. Atrakcyjne właściwości wspomnianych układów związane są z uporządkowaniem atomowym dalekiego zasięgu, które powstaje w układzie na drodze migracji atomów odbywającej się za pośrednictwem wakancji. Eksperymentalnie stwierdzono, że w związku NiAl zawierającym kilka rzędów wielkości więcej wakancji niż Ni3Al proces porządkowania atomowego przebiega znacznie wolniej. Przeprowadzone badania miały na celu weryfikację hipotezy, iż przyczyn ą obserwowanego zjawiska jest defekt potrójny - w specyficzny sposób "pułapkujący" wakancje powstające w związku NiAl. W ramach studium nad przyczyną wspomnianego zjawiska opracowany został oparty na symulacjach Monte Carlo model procesu tworzenia defektów antystrukturalnych w układzie z nadstrukturą B2 wykazującym tendencję do tworzenia defektów potrójnych. Realizacja projektu przebiegała w dwóch etapach: (i) Opracowanie analitycznego i symulacyjnego modelu termodynamicznego do wyznaczania równowagowej koncentracji wakancji. (ii) Symulacja relaksacji "porządek-porządek" w układzie z nadstrukturą B2 metodami "Kinetic Monte Carlo" przy uwzględnieniu równowagowej koncentracji wakancji wyznaczanej metodami opracowanymi w etapie (i). W ramach opracowanego modelu dwuskładnikowego związku międzymetalicznego AB opartego na nadstrukturze typu B2 przebadano naturę defektu potrójnego jak i jego wpływ na kinetykę przemian typu "porządek-porządek". Symulacyjne rozwiązanie modelu termodynamicznego tworzenia wakancji pozwoliło na przebadanie specyficznej korelacji tworzenia defektów punktowych - rozpoznano istnienie defektu potrójnego w wymodelowanym układzie. W ramach symulacji kinetyk typu "porządek-porządek" wykryto możliwą przyczynę zwolnienia procesów rozporządkowania (zarejstrowaną eksperymentalnie dla układu B2 NiAl ) związaną z asymetrią tworzenia defektów punktowych w sieci krystalicznej (defekt potrójny). Tym samym cel pracy został osiągnięty

Atomization of correlated molecular-hydrogen chain: A fully microscopic Variational Monte-Carlo solution

We discuss electronic properties and their evolution for the linear chain of $H_2$ molecules in the presence of a uniform external force $f$ acting along the chain. The system is described by an extended Hubbard model within a fully microscopic approach. Explicitly, the microscopic parameters describing the intra- and inter-site Coulomb interactions are determined together with the hopping integrals by optimizing the system ground state energy and the single-particle wave functions in the correlated state. The many-body wave function is taken in the Jastrow form and the Variational Monte-Carlo (VMC) method is used in combination with an ab initio approach to determine the energy. Both the effective Bohr radii of the renormalized single-particle wave functions and the many-body wave function parameters are determined for each $f$. Hence, the evolution of the system can be analyzed in detail as a function of the equilibrium intermolecular distance, which in turn is determined for each $f$ value. The transition to the atomic state, including the Peierls distortion stability, can thus be studied in a systematic manner, particularly near the threshold of the dissociation of the molecular into atomic chain. The computational reliability of VMC approach is also estimated

H2H_2 and (H2)2(H_2)_2 molecules with an ab initio optimization of wave functions in correlated state: Electron-proton couplings and intermolecular microscopic parameters

The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron--ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to the solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for $2 \times H_2$ rectangular configurations.Comment: 14 pages, 14 figures, 6 table

Dot-ring nanostructure: rigorous analysis of many-electron effects

We discuss the quantum dot-ring nanostructure (DRN) as canonical example of a nanosystem, for which the interelectronic interactions can be evaluated exactly. The system has been selected due to its tunability, i.e., its electron wave functions can be modified much easier than in, e.g., quantum dots. We determine many-particle states for Ne = 2 and 3 electrons and calculate the 3- and 4-state interaction parameters, and discuss their importance. For that purpose, we combine the first- and second-quantization schemes and hence are able to single out the component single-particle contributions to the resultant many-particle state. The method provides both the ground- and the first-excited-state energies, as the exact diagonalization of the many-particle Hamiltonian is carried out. DRN provides one of the few examples for which one can determine theoretically all interaction microscopic parameters to a high accuracy. Thus the evolution of the single-particle vs. many-particle contributions to each state and its energy can be determined and tested with the increasing system size. In this manner, we contribute to the wave-function engineering with the interactions included for those few-electron systems

Chemical ordering kinetics and thermal vacancy thermodynamics in B2 binary intermetallics: simulation study

Les alliages intermétalliques de structure B2 sont des matériaux prometteurs pour leurs propriétés physiques. Une concentration anormalement élevée de lacunes est observée dans les alliages B2 très ordonnés. Les sauts atomiques élémentaires ayant lieu via des sauts de lacunes, il est surprenant que la vitesse d’évolution de l’ordre est bien plus basse dans NiAl ordonné B2 – système où la concentration de lacunes est très haute – que dans le système L12 – Ni3Al où la concentration de lacunes est bien plus basse. Ce phénomène a souvent été expliqué par l’existence dans cette structure de défauts triples, où les lacunes sont en grande partie piégées sur le sous-réseau du nickel en corrélation avec des antisites de Ni (atomes de Ni sur le sous-réseau Al), avec deux lacunes pour un antisite. Le but général de cette thèse a été d’élaborer une méthodologie pour les simulations par méthode Monte-Carlo des cinétiques de transformation structurale de ces systèmes. Il a été nécessaire de développer un modèle thermodynamique qui permette de déterminer la concentration de lacunes d’équilibre – la dépendance en température de cette concentration ne pouvant plus être négligée. Des simulations Monte-Carlo cinétiques cohérentes peuvent ensuite être effectuées. Ces modélisations ont été faites avec un hamiltonien d’Ising et avec un hamiltonien multi-atomes de la méthode de l’atome entouré (embedded atom method). Les résultats obtenus sont en bon accord avec les observations expérimentales : l’évolution lente du système est due au manque d’efficacité statistique des sauts effectués (beaucoup d’aller-retours) après le premier stade rapide de génération des défauts triples.Intermetallics based on the B2 superstructure are very promising for their physical properties. An unusual high vacancy concentration is observed in highly ordered systems. Whereas elementary atomic jumps occur via a vacancy mechanism, surprisingly the rate of chemical ordering processes is much lower for B2 – NiAl superstructure – with relatively very high vacancy concentration – in comparison to the system with low vacancy concentration (L12 - Ni3Al). That phenomenon was often explained by the means of so called „triple defect” – where vacancies are mostly „trapped” on the Ni sub-lattice and correlated with creation of Ni antisites (Ni atoms residing on the Al sub-lattice), with statistically two vacancies per one antisite. The general aim of this thesis was to elaborate a methodology for kinetic simulations by Monte-Carlo methods of structural transformations in these systems. Therefore it was necessary to develop a thermodynamic model which allows finding equilibrium vacancy concentration – as the thermal dependency of vacancy concentration cannot be neglected. Consistent Kinetic Monte-Carlo simulations could be next realized. They were made using either an Ising-type Hamiltonian or the many body potentials of the Embedded Atom Method. The results are in good agreement with the experimental observations: the slow evolution of the system is due to the statistical inefficiency of jumps performed (many return jumps) after the extremely fast stage of generation of triple defects

Cinétiques d'ordre chimique et thermodynamique des lacunes thermiques dans les intermétalliques binaires B2 : une étude par simulation

Les alliages intermétalliques de structure B2 sont des matériaux prometteurs pour leurs propriétés physiques. Une concentration anormalement élevée de lacunes est observée dans les alliages B2 très ordonnés. Les sauts atomiques élémentaires ayant lieu viaIntermetallics based on the B2 superstructure are very promising for their physical properties. An unusual high vacancy concentration is observed in highly ordered systems. Whereas elementary atomic jumps occur via a vacancy mechanism, surprisingly the r

Superconductivity and intra-unit-cell electronic nematic phase in the three-band model of cuprates

The intra-unit-cell nematic phase is studied within the three-band Emery model of the cuprates by using the diagrammatic expansion of the Gutzwiller wave function (DE-GWF). According to our analysis a spontaneous rotational (C4) symmetry breaking of the electronic wave function, leading to the nematic behavior, can appear due to electron correlations induced mainly by the onsite Coulomb repulsion, even in the absence of the corresponding intersite oxygen–oxygen repulsion term. The latter has been considered as the triggering factor of the nematic state formation in a number of previous studies. Also, we show that at the transition to the nematic phase, electron concentration transfer from d- to p-orbitals takes place, apart from the usually discussed $p_x∕p_y$ polarization. The nematicity appears in a similar doping range as the paired phase, showing that both phases may have a common origin, even though they compete. As we show a coexistence region of both superconductivity and nematicity appears in a relatively wide doping range. The results are discussed in view of the experimental findings corresponding to the relation between nematicity and pseudogap behavior