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The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment strategies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on current case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.
Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities
(2021)
The distinct ways the COVID-19 pandemic has been unfolding in different countries and regions suggest that local societal and governmental structures play an important role not only for the baseline infection rate, but also for short and long-term reactions to the outbreak. We propose to investigate the question of how societies as a whole, and governments in particular, modulate the dynamics of a novel epidemic using a generalization of the SIR model, the reactive SIR (short-term and long-term reaction) model. We posit that containment measures are equivalent to a feedback between the status of the outbreak and the reproduction factor. Short-term reaction to an outbreak corresponds in this framework to the reaction of governments and individuals to daily cases and fatalities. The reaction to the cumulative number of cases or deaths, and not to daily numbers, is captured in contrast by long-term reaction. We present the exact phase space solution of the controlled SIR model and use it to quantify containment policies for a large number of countries in terms of short and long-term control parameters. We find increased contributions of long-term control for countries and regions in which the outbreak was suppressed substantially together with a strong correlation between the strength of societal and governmental policies and the time needed to contain COVID-19 outbreaks. Furthermore, for numerous countries and regions we identified a predictive relation between the number of fatalities within a fixed period before and after the peak of daily fatality counts, which allows to gauge the cumulative medical load of COVID-19 outbreaks that should be expected after the peak. These results suggest that the proposed model is applicable not only for understanding the outbreak dynamics, but also for predicting future cases and fatalities once the effectiveness of outbreak suppression policies is established with sufficient certainty. Finally, we provide a web app (https://itp.uni-frankfurt.de/covid-19/) with tools for visualising the phase space representation of real-world COVID-19 data and for exporting the preprocessed data for further analysis.
Recent experimental findings have reported the presence of unconventional charge orders in the enlarged (2 × 2) unit-cell of kagome metals AV3Sb5 (A = K, Rb, Cs) and hinted towards specific topological signatures. Motivated by these discoveries, we investigate the types of topological phases that can be realized in such kagome superlattices. In this context, we employ a recently introduced statistical method capable of constructing topological models for any generic lattice. By analyzing large data sets generated from symmetry-guided distributions of randomized tight-binding parameters, and labeled with the corresponding topological index, we extract physically meaningful information. We illustrate the possible real-space manifestations of charge and bond modulations and associated flux patterns for different topological classes, and discuss their relation to present theoretical predictions and experimental signatures for the AV3Sb5 family. Simultaneously, we predict higher-order topological phases that may be realized by appropriately manipulating the currently known systems.
Electron beam-induced deposition with tungsten hexacarbonyl W(CO)6 as precursors leads to granular deposits with varying compositions of tungsten, carbon and oxygen. Depending on the deposition conditions, the deposits are insulating or metallic. We employ an evolutionary algorithm to predict the crystal structures starting from a series of chemical compositions that were determined experimentally. We show that this method leads to better structures than structural relaxation based on estimated initial structures. We approximate the expected amorphous structures by reasonably large unit cells that can accommodate local structural environments that resemble the true amorphous structure. Our predicted structures show an insulator-to-metal transition close to the experimental composition at which this transition is actually observed and they also allow comparison with experimental electron diffraction patterns.
The description of quantized collective excitations stands as a landmark in the quantum theory of condensed matter. A prominent example occurs in conventional magnets, which support bosonic magnons—quantized harmonic fluctuations of the ordered spins. In striking contrast is the recent discovery that strongly spin-orbital-coupled magnets, such as α-RuCl3, may display a broad excitation continuum inconsistent with conventional magnons. Due to incomplete knowledge of the underlying interactions unraveling the nature of this continuum remains challenging. The most discussed explanation refers to a coherent continuum of fractional excitations analogous to the celebrated Kitaev spin liquid. Here, we present a more general scenario. We propose that the observed continuum represents incoherent excitations originating from strong magnetic anharmonicity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of α-RuCl3 and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state.
Motivated by recent experimental suggestions of charge-order-driven ferroelectricity in organic charge-transfer salts, such as κ-(BEDT-TTF)2Cu[N(CN)2]Cl, we investigate magnetic and charge-ordered phases that emerge in an extended two-orbital Hubbard model on the anisotropic triangular lattice at 3/4 filling. This model takes into account the presence of two organic BEDT-TTF molecules, which form a dimer on each site of the lattice, and includes short-range intramolecular and intermolecular interactions and hoppings. By using variational wave functions and quantum Monte Carlo techniques, we find two polar states with charge disproportionation inside the dimer, hinting to ferroelectricity. These charge-ordered insulating phases are stabilized in the strongly correlated limit and their actual charge pattern is determined by the relative strength of intradimer to interdimer couplings. Our results suggest that ferroelectricity is not driven by magnetism, since these polar phases can be stabilized also without antiferromagnetic order and provide a possible microscopic explanation of the experimental observations. In addition, a conventional dimer-Mott state (with uniform density and antiferromagnetic order) and a nonpolar charge-ordered state (with charge-rich and charge-poor dimers forming a checkerboard pattern) can be stabilized in the strong-coupling regime. Finally, when electron–electron interactions are weak, metallic states appear, with either uniform charge distribution or a peculiar 12-site periodicity that generates honeycomb-like charge order.
One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which—regardless of its simplicity—is exactly solvable only in a few limiting cases and approximate many-body methods are required for its solution. In this review, an overview on the non-perturbative two-particle self-consistent method (TPSC), which was originally introduced to describe the electronic properties of the single-band Hubbard model, is presented. A detailed derivation of the multi-orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean-field theory results are discussed.
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
The phase diagram of the square lattice bilayer Hubbard model: a variational Monte Carlo study
(2014)
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
We present experimental results and theoretical simulations of the adsorption behavior of the metal–organic precursor Co2(CO)8 on SiO2 surfaces after application of two different pretreatment steps, namely by air plasma cleaning or a focused electron beam pre-irradiation. We observe a spontaneous dissociation of the precursor molecules as well as autodeposition of cobalt on the pretreated SiO2 surfaces. We also find that the differences in metal content and relative stability of these deposits depend on the pretreatment conditions of the substrate. Transport measurements of these deposits are also presented. We are led to assume that the degree of passivation of the SiO2 surface by hydroxyl groups is an important controlling factor in the dissociation process. Our calculations of various slab settings, using dispersion-corrected density functional theory, support this assumption. We observe physisorption of the precursor molecule on a fully hydroxylated SiO2 surface (untreated surface) and chemisorption on a partially hydroxylated SiO2 surface (pretreated surface) with a spontaneous dissociation of the precursor molecule. In view of these calculations, we discuss the origin of this dissociation and the subsequent autocatalysis.
Oxygen vacancies in strontium titanate surfaces (SrTiO3) have been linked to the presence of a two-dimensional electron gas with unique behavior. We perform a detailed density functional theory study of the lattice and electronic structure of SrTiO3 slabs with multiple oxygen vacancies, with a main focus on two vacancies near a titanium dioxide terminated SrTiO3 surface. We conclude based on total energies that the two vacancies preferably inhabit the first two layers, i.e. they cluster vertically, while in the direction parallel to the surface, the vacancies show a weak tendency towards equal spacing. Analysis of the nonmagnetic electronic structure indicates that oxygen defects in the surface TiO2 layer lead to population of Ti ${{t}_{2g}}$ states and thus itinerancy of the electrons donated by the oxygen vacancy. In contrast, electrons from subsurface oxygen vacancies populate Ti eg states and remain localized on the two Ti ions neighboring the vacancy. We find that both the formation of a bound oxygen-vacancy state composed of hybridized Ti 3eg and 4p states neighboring the oxygen vacancy as well as the elastic deformation after extracting oxygen contribute to the stabilization of the in-gap state.
Motivated by recently reported magnetic-field induced topological phases in ultracold atoms and correlated Moiré materials, we investigate topological phase transitions in a minimal model consisting of interacting spinless fermions described by the Hofstadter model on a square lattice. For interacting lattice Hamiltonians in the presence of a commensurate magnetic flux it has been demonstrated that the quantized Hall conductivity is constrained by a Lieb-Schultz-Mattis (LSM)-type theorem due to magnetic translation symmetry. In this work, we revisit the validity of the theorem for such models and establish that a topological phase transition from a topological to a trivial insulating phase can be realized but must be accompanied by spontaneous magnetic translation symmetry breaking caused by charge ordering of the spinless fermions. To support our findings, the topological phase diagram for varying interaction strength is mapped out numerically with exact diagonalization for different flux quantum ratios and band fillings using symmetry indicators. We discuss our results in the context of the LSM-type theorem.
he family of cubic noncentrosymmetric 3-4-3 compounds has become a fertile ground for the discovery of novel correlated metallic and insulating phases. Here, we report the synthesis of a new heavy fermion compound, Ce3Bi4Ni3. It is an isoelectronic analog of the prototypical Kondo insulator Ce3Bi4Pt3 and of the recently discovered Weyl-Kondo semimetal Ce3Bi4Pd3. In contrast to the volume-preserving Pt-Pd substitution, structural and chemical analyses reveal a positive chemical pressure effect in Ce3Bi4Ni3 relative to its heavier counterparts. Based on the results of electrical resistivity, Hall effect, magnetic susceptibility, and specific heat measurements, we identify an energy gap of 65–70 meV, about eight times larger than that in Ce3Bi4Pt3 and about 45 times larger than that of the Kondo-insulating background hosting the Weyl nodes in Ce3Bi4Pd3. We show that this gap as well as other physical properties do not evolve monotonically with increasing atomic number, i.e., in the sequence Ce3Bi4Ni3−Ce3Bi4Pd3−Ce3Bi4Pt3, but instead with increasing partial electronic density of states of the 𝑑 orbitals at the Fermi energy. This work opens the possibility to investigate the conditions under which topological states develop in this series of strongly correlated 3-4-3 materials.
Heterostructures of graphene in proximity to magnetic insulators open the possibility to investigate exotic states emerging from the interplay of magnetism, strain and charge transfer between the layers. Recent reports on the growth of self-integrated atomic wires of β-RuCl3 on graphite suggest these materials as versatile candidates to investigate these effects. Here we present detailed first principles calculations on the charge transfer and electronic structure of β-RuCl3/heterostructures and provide a comparison with the work function analysis of the related honeycomb family members α-RuX3 (X = Cl,Br,I). We find that proximity of the two layers leads to a hole-doped graphene and electron-doped RuX3 in all cases, which is sensitively dependent on the distance between the two layers. Furthermore, strain effects due to lattice mismatch control the magnetization which itself has a strong effect on the charge transfer. Charge accumulation in β-RuCl3 strongly drops away from the chain making such heterostructures suitable candidates for sharp interfacial junctions in graphene-based devices.
Understanding the physics of strongly correlated electronic systems has been a central issue in condensed matter physics for decades. In transition metal oxides, strong correlations characteristic of narrow d bands are at the origin of remarkable properties such as the opening of Mott gap, enhanced effective mass, and anomalous vibronic coupling, to mention a few. SrVO3 with V4+ in a 3d1 electronic configuration is the simplest example of a 3D correlated metallic electronic system. Here, the authors' focus on the observation of a (roughly) quadratic temperature dependence of the inverse electron mobility of this seemingly simple system, which is an intriguing property shared by other metallic oxides. The systematic analysis of electronic transport in SrVO3 thin films discloses the limitations of the simplest picture of e–e correlations in a Fermi liquid (FL); instead, it is shown show that the quasi-2D topology of the Fermi surface (FS) and a strong electron–phonon coupling, contributing to dress carriers with a phonon cloud, play a pivotal role on the reported electron spectroscopic, optical, thermodynamic, and transport data. The picture that emerges is not restricted to SrVO3 but can be shared with other 3d and 4d metallic oxides.
Under temperature or pressure tuning, tetragonal EuPd2Si2 is known to undergo a valence transition from nearly divalent to nearly trivalent Eu accompanied by a volume reduction. Albeit intensive work, its origin is not yet completely understood. Here, we investigate the mechanism of the valence transition under volume compression by density functional theory calculations (DFT). Our analysis suggests that the transition is a consequence of an enhanced c−f hybridization between localized Eu 4f states and itinerant conduction states (Eu 5d, Pd 4d, and Si 3p) where the interplay of the electronic bandwidth, crystal field environment, Coulomb repulsion, Hund's coupling and spin-orbit coupling plays a crucial role for the transition to happen. The change in the electronic structure is intimately related to the volume reduction where Eu-Pd(Si) bond lengths shorten. In a next step we compare our DFT results to surface-sensitive photoemission data in which the mixed-valent properties of EuPd2Si2 are reflected in a simultaneous observation of divalent and trivalent signals from the Eu 4f shell.
Under temperature or pressure tuning, tetragonal EuPd2Si2 is known to undergo a valence transition from nearly divalent to nearly trivalent Eu accompanied by a volume reduction. Albeit intensive work, its microscopic origin is still being discussed. Here, we investigate the mechanism of the valence transition under volume compression by ab initio density functional theory (DFT) calculations. Our analysis of the electronic and magnetic properties of EuPd2Si2 when approaching the valence transition shows an enhanced c-f hybridization between localized Eu 4f states and itinerant conduction states (Eu 5d, Pd 4d, and Si 3p) where an electronic charge redistribution takes place. We observe that the change in the electronic structure is intimately related to the volume reduction where Eu-Pd(Si) bond lengths shorten and, for the transition to happen, we trace the delicate balance between electronic bandwidth, crystal field splitting, Coulomb repulsion, Hund's coupling and spin-orbit coupling. In a next step we compare and benchmark our DFT results to surface-sensitive photoemission data in which the mixed-valent properties of EuPd2Si2 are reflected in a simultaneous observation of divalent and trivalent signals from the Eu 4f shell. The study serves as well to explore the limits of density functional theory and the choice of exchange correlation functionals to describe such a phenomenon as a valence transition.
The antiferromagnet and semimetal EuCd2As2 has recently attracted a lot of attention due to a wealth of topological phases arising from the interplay of topology and magnetism. In particular, the presence of a single pair of Weyl points is predicted for a ferromagnetic configuration of Eu spins along the c-axis in EuCd2As2. In the search for such phases, we investigate here the effects of hydrostatic pressure in EuCd2As2. For that, we present specific heat, transport and μSR measurements under hydrostatic pressure up to ∼2.5GPa, combined with {\it ab initio} density functional theory (DFT) calculations. Experimentally, we establish that the ground state of EuCd2As2 changes from in-plane antiferromagnetic (AFMab) to ferromagnetic at a critical pressure of ≈2\,GPa, which is likely characterized by the moments dominantly lying within the ab plane (FMab). The AFMab-FMab transition at such a relatively low pressure is supported by our DFT calculations. Furthermore, our experimental and theoretical results indicate that EuCd2As2 moves closer to the sought-for FMc state (moments ∥ c) with increasing pressure further. We predict that a pressure of ≈\,23\,GPa will stabilize the FMc state, if Eu remains in a 2+ valence state. Thus, our work establishes hydrostatic pressure as a key tuning parameter that (i) allows for a continuous tuning between magnetic ground states in a single sample of EuCd2As2 and (ii) enables the exploration of the interplay between magnetism and topology and thereby motivates a series of future experiments on this magnetic Weyl semimetal.
The family of cubic noncentrosymmetric 3-4-3 compounds has become a fertile ground for the discovery of novel correlated metallic and insulating phases. Here, we report the synthesis of a new heavy fermion compound, Ce3Bi4Ni3. It is an isoelectronic analog of the prototypical Kondo insulator Ce3Bi4Pt3 and of the recently discovered Weyl-Kondo semimetal Ce3Bi4Pd3. In contrast to the volume-preserving Pt-Pd substitution, structural and chemical analyses reveal a positive chemical pressure effect in Ce3Bi4Ni3 relative to its heavier counterparts. Based on the results of electrical resistivity, Hall effect, magnetic susceptibility, and specific heat measurements, we identify an energy gap of 65-70 meV, about eight times larger than that in Ce3Bi4Pt3 and about 45 times larger than that of the Kondo-insulating background hosting the Weyl nodes in Ce3Bi4Pd3. We show that this gap as well as other physical properties do not evolve monotonically with increasing atomic number, i.e., in the sequence Ce3Bi4Ni3-Ce3Bi4Pd3-Ce3Bi4Pt3, but instead with increasing partial electronic density of states of the d orbitals at the Fermi energy. To understand under which condition topological states form in these materials is a topic for future studies.