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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.
Type-II multiferroic materials, in which ferroelectric polarization is induced by inversion non-symmetric magnetic order, promise new and highly efficient multifunctional applications based on mutual control of magnetic and electric properties. However, to date this phenomenon is limited to low temperatures. Here we report giant pressure-dependence of the multiferroic critical temperature in CuBr2: at 4.5 GPa it is enhanced from 73.5 to 162 K, to our knowledge the highest TC ever reported for non-oxide type-II multiferroics. This growth shows no sign of saturating and the dielectric loss remains small under these high pressures. We establish the structure under pressure and demonstrate a 60\% increase in the two-magnon Raman energy scale up to 3.6 GPa. First-principles structural and magnetic energy calculations provide a quantitative explanation in terms of dramatically pressure-enhanced interactions between CuBr2 chains. These large, pressure-tuned magnetic interactions motivate structural control in cuprous halides as a route to applied high-temperature multiferroicity.
Formation of Hubbard-like bands as a fingerprint of strong electron-electron interactions in FeSe
(2017)
We use angle-resolved photo-emission spectroscopy (ARPES) to explore the electronic structure of single crystals of FeSe over a wide range of binding energies and study the effects of strong electron-electron correlations. We provide evidence for the existence of "Hubbard-like bands" at high binding energies consisting of incoherent many-body excitations originating from Fe 3d states in addition to the renormalized quasiparticle bands near the Fermi level. Many high energy features of the observed ARPES data can be accounted for when incorporating effects of strong local Coulomb interactions in calculations of the spectral function via dynamical mean-field theory, including the formation of a Hubbard-like band. This shows that over the energy scale of several eV, local correlations arising from the on-site Coulomb repulsion and Hund's coupling are essential for a proper understanding of the electronic structure of FeSe and other related iron based superconductors.
In the search for novel organic charge transfer salts with variable degrees of charge transfer we have studied the effects of two modifications of the recently synthesized donor–acceptor system [tetramethoxypyrene (TMP)]–[tetracyanoquinodimethane (TCNQ)]. One is of chemical nature by substituting the acceptor TCNQ molecules by F4TCNQ molecules. The second consists in simulating the application of uniaxial pressure along the stacking axis of the system. In order to test the chemical substitution, we have grown single crystals of the TMP–F4TCNQ complex and analyzed its electronic structure via electronic transport measurements, ab initio density functional theory (DFT) calculations and UV/VIS/IR absorption spectroscopy. This system shows an almost ideal geometrical overlap of nearly planar molecules stacked alternately (mixed stack) and this arrangement is echoed by a semiconductor-like transport behavior with an increased conductivity along the stacking direction. This is in contrast to TMP–TCNQ which shows a less pronounced anisotropy and a smaller conductivity response. Our band structure calculations confirm the one-dimensional behavior of TMP–F4TCNQ with pronounced dispersion only along the stacking axis. Infrared measurements illustrating the C[triple bond, length as m-dash]N vibration frequency shift in F4TCNQ suggest however no improvement in the degree of charge transfer in TMP–F4TCNQ with respect to TMP–TCNQ. In both complexes about 0.1e is transferred from TMP to the acceptor. Concerning the pressure effect, our DFT calculations on the designed TMP–TCNQ and TMP–F4TCNQ structures under different pressure conditions show that application of uniaxial pressure along the stacking axis of TMP–TCNQ may be the route to follow in order to obtain a much more pronounced charge transfer.
Controlling and understanding electron correlations in quantum matter is one of the most challenging tasks in materials engineering. In the past years a plethora of new puzzling correlated states have been found by carefully stacking and twisting two-dimensional van der Waals materials of different kind. Unique to these stacked structures is the emergence of correlated phases not foreseeable from the single layers alone. In Ta-dichalcogenide heterostructures made of a good metallic “1H”- and a Mott insulating “1T”-layer, recent reports have evidenced a cross-breed itinerant and localized nature of the electronic excitations, similar to what is typically found in heavy fermion systems. Here, we put forward a new interpretation based on first-principles calculations which indicates a sizeable charge transfer of electrons (0.4-0.6 e) from 1T to 1H layers at an elevated interlayer distance. We accurately quantify the strength of the interlayer hybridization which allows us to unambiguously determine that the system is much closer to a doped Mott insulator than to a heavy fermion scenario. Ta-based heterolayers provide therefore a new ground for quantum-materials engineering in the regime of heavily doped Mott insulators hybridized with metallic states at a van der Waals distance.
Critical spin liquid versus valence-bond glass in a triangular-lattice organic antiferromagnet
(2019)
In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet κ-(ET)2Cu2(CN)3 has been extensively discussed as a quantum spin liquid (QSL) candidate. The description of its low temperature properties has become, however, a particularly challenging task. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Here we highlight significant deviations of the experimental observations from a quantum critical scenario by performing a microscopic analysis of all anisotropic contributions, including Dzyaloshinskii–Moriya and multi-spin scalar chiral interactions. Instead, we show that disorder-induced spin defects provide a comprehensive explanation of the low-temperature properties. These spins are attributed to valence bond defects that emerge spontaneously as the QSL enters a valence-bond glass phase at low temperature. This theoretical treatment is applicable to a general class of frustrated magnetic systems and has important implications for the interpretation of magnetic torque, nuclear magnetic resonance, thermal transport and thermodynamic experiments.
Deconfinement of Mott localized electrons into topological and spin–orbit-coupled Dirac fermions
(2020)
The interplay of electronic correlations, spin–orbit coupling and topology holds promise for the realization of exotic states of quantum matter. Models of strongly interacting electrons on honeycomb lattices have revealed rich phase diagrams featuring unconventional quantum states including chiral superconductivity and correlated quantum spin Hall insulators intertwining with complex magnetic order. Material realizations of these electronic states are, however, scarce or inexistent. In this work, we propose and show that stacking 1T-TaSe2 into bilayers can deconfine electrons from a deep Mott insulating state in the monolayer to a system of correlated Dirac fermions subject to sizable spin–orbit coupling in the bilayer. 1T-TaSe2 develops a Star-of-David charge density wave pattern in each layer. When the Star-of-David centers belonging to two adyacent layers are stacked in a honeycomb pattern, the system realizes a generalized Kane–Mele–Hubbard model in a regime where Dirac semimetallic states are subject to significant Mott–Hubbard interactions and spin–orbit coupling. At charge neutrality, the system is close to a quantum phase transition between a quantum spin Hall and an antiferromagnetic insulator. We identify a perpendicular electric field and the twisting angle as two knobs to control topology and spin–orbit coupling in the system. Their combination can drive it across hitherto unexplored grounds of correlated electron physics, including a quantum tricritical point and an exotic first-order topological phase transition.
Electronic systems living on Archimedean lattices such as kagome and square–octagon networks are presently being intensively discussed for the possible realization of topological insulating phases. Coining the most interesting electronic topological states in an unbiased way is however not straightforward due to the large parameter space of possible Hamiltonians. A possible approach to tackle this problem is provided by a recently developed statistical learning method (Mertz and Valentí in Phys Rev Res 3:013132, 2021. https://doi.org/10.1103/PhysRevResearch.3.013132), based on the analysis of a large data sets of randomized tight-binding Hamiltonians labeled with a topological index. In this work, we complement this technique by introducing a feature engineering approach which helps identifying polynomial combinations of Hamiltonian parameters that are associated with non-trivial topological states. As a showcase, we employ this method to investigate the possible topological phases that can manifest on the square–octagon lattice, focusing on the case in which the Fermi level of the system lies at a high-order van Hove singularity, in analogy to recent studies of topological phases on the kagome lattice at the van Hove filling.
The interaction of trimethyl(methylcyclopentadienyl)platinum(IV) ((C5H4CH3)Pt(CH3)3) molecules on fully and partially hydroxylated SiO2 surfaces, as well as the dynamics of this interaction were investigated using density functional theory (DFT) and finite temperature DFT-based molecular dynamics simulations. Fully and partially hydroxylated surfaces represent substrates before and after electron beam treatment and this study examines the role of electron beam pretreatment on the substrates in the initial stages of precursor dissociation and formation of Pt deposits. Our simulations show that on fully hydroxylated surfaces or untreated surfaces, the precursor molecules remain inactivated while we observe fragmentation of (C5H4CH3)Pt(CH3)3 on partially hydroxylated surfaces. The behavior of precursor molecules on the partially hydroxylated surfaces has been found to depend on the initial orientation of the molecule and the distribution of surface active sites. Based on the observations from the simulations and available experiments, we discuss possible dissociation channels of the precursor.
The aim of the present overview article is to raise awareness of an essential aspect that is usually not accounted for in the modelling of electron transport for focused-electron-beam-induced deposition (FEBID) of nanostructures: Surface excitations are on the one hand responsible for a sizeable fraction of the intensity in reflection-electron-energy-loss spectra for primary electron energies of up to a few kiloelectronvolts and, on the other hand, they play a key role in the emission of secondary electrons from solids, regardless of the primary energy. In this overview work we present a general perspective of recent works on the subject of surface excitations and on low-energy electron transport, highlighting the most relevant aspects for the modelling of electron transport in FEBID simulations.
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 use the topological heavy fermion (THF) model and its Kondo Lattice (KL) formulation to study the symmetric Kondo state in twisted bilayer graphene. Via a large-N approximation, we find a symmetric Kondo (SK) state in KL mode at fillings ν=0,±1,±2. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at ν=0,±1,±2,±3, we also find a similar symmetric state. We study the stability of the symmetric state by comparing its energy with the ordered states and find the ordered states to have lower energy. However, moving away from integer fillings by doping holes to the light bands, we find the energy difference is reduced, which suggests the loss of ordering and a tendency towards Kondo screening. In order to include many-body effects beyond the mean-field approximation, we perform dynamical mean-field theory (DMFT) calculations on the THF model. We find the spin susceptibility follows a Curie behavior at ν=0,±1,±2 down to ∼2K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At non-integer filling ν=±0.5,±0.8,±1.2 DMFT shows deviations from a 1/T-susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a C3z-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C3z symmetry) can be stabilized at sufficiently large strain at ν=0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at non-integer fillings or by applying strain.