Real-space Model Research Articles

Glasslike caging with random planes.

The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics in the same way that the random energy model clarifies spin glass behavior would therefore be beneficial. Here we propose such a real-space model that is amenable to infinite-dimensional d→∞ analysis and is exactly solvable in finite d in some regimes. By joining analysis with numerical simulations, we uncover geometrical signatures of the dynamical and jamming transitions and obtain insight into the origin of activated processes. Translating these findings into the context of standard glass formers further reveals the role played by nonconvexity in the emergence of Gardner and jamming physics.

Numerical model for linear stimulated Raman scattering in inhomogeneous plasmas

Numerical model for calculating convective gains and absolute thresholds of stimulated Raman scattering (SRS) in inhomogeneous plasmas is constructed based on the Fourier-space method. The model is valid for arbitrary density profiles and scattering geometries, including both backscattering and side scattering. It is shown that 90 deg side scatter has a lower absolute threshold than other scattering geometries. Backscatter, on the other hand, has a relatively large absolute threshold under conventional direct-drive ignition conditions. For a parabolic density profile, the absolute threshold of backscatter decreases dramatically at the peak of parabola, but is still much larger than that of side scatter. We also discuss the absolute thresholds of side scatter under different density profiles, showing not big differences with the linear density profile as well as the analytic formulas. Convective gains, however, are sensitive to the density profiles and collisional damping. The k-space numerical model is verified via analytic formulas and real-space envelope model, and it offers us new perspective on the scattering angles compared with previous models for SRS.

Revisiting the density profile of the fuzzy sphere model for microgel colloids.

Common neutral polymer microgels exhibit an inhomogeneous density profile with a gradual decay that is commonly described using the fuzzy sphere model. The model is based on the idea of convolving the collapsed solid sphere profile with a Gaussian to describe inhomogeneous swelling of the microgel in a good solvent. Here we show that the corresponding density profile in real space used in several recent works - such as in super-resolution microscopy - is different from the fuzzy sphere model, and we explain how to correctly transition between reciprocal space modelling to real space. Our work aims to clarify the application of the model so that errors can be avoided in the future. Our discussion is also crucial when comparing alternative real-space models for the density profile with the established fuzzy sphere model.

Real-space model for activated processes in rejuvenation and memory behavior of glassy systems.

We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed system, to analyze rejuvenation and memory effects during aging after a hard quench. In this model, neighboring particles on a lattice aggregate through local interactions into clusters that fragment with a probability based on their size. Despite the simplicity of the cluster model, it has been shown to reproduce salient observables of the aging dynamics in colloidal systems, such as those accounting for particle mobility and displacements. Here, we probe the model for more complex quench protocols and show that it exhibits rejuvenation and memory effects similar to those attributed to the complex hierarchical structure of a glassy energy landscape.

Real-space tight-binding model for twisted bilayer graphene based on mapped Wannier functions

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π-bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting.

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors.

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order incuprates.

High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation (SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved (k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Strategy to simulate and fit 2D grazing-incidence small-angle X-ray scattering patterns of nanostructured thin films.

Grazing-incidence small-angle X-ray scattering (GISAXS) is a widely used method for the characterization of the nanostructure of supported thin films and enables time-resolved in situ measurements. The 2D scattering patterns contain detailed information about the nanostructures within the film and at its surface. However, this information is distorted not only by the reflection of the X-ray beam at the substrate-film interface and its refraction at the film surface but also by scattering of the substrate, the sample holder and other types of parasitic background scattering. In this work, a new, efficient strategy to simulate and fit 2D GISAXS patterns that explicitly includes these effects is introduced and demonstrated for (i) a model case nanostructured thin film on a substrate and (ii) experimental data from a microphase-separated block copolymer thin film. To make the protocol efficient, characteristic linecuts through the 2D GISAXS patterns, where the different contributions dominate, are analysed. The contributions of the substrate and the parasitic background scattering - which ideally are measured separately - are determined first and are used in the analysis of the 2D GISAXS patterns of the nanostructured, supported film. The nanostructures at the film surface and within the film are added step by step to the real-space model of the simulation, and their structural parameters are determined by minimizing the difference between simulated and experimental scattering patterns in the selected linecuts. Although in the present work the strategy is adapted for and tested with BornAgain, it can be easily used with other types of simulation software. The strategy is also applicable to grazing-incidence small-angle neutron scattering.

Excitons and Their Fine Structure in Lead Halide Perovskite Nanocrystals from Atomistic GW/BSE Calculations

Atomistically detailed computational studies of nanocrystals, such as those derived from the promising lead-halide perovskites, are challenging due to the large number of atoms and lack of symmetries to exploit. Here, focusing on methylammonium lead iodide nanocrystals, we combine a real-space tight binding model with the GW approximation to the self-energy and obtain exciton wave functions and absorption spectra via solutions of the associated Bethe–Salpeter equation. We find that the size dependence of carrier confinement, dielectric contrast, electron–hole exchange, and exciton binding energies has a strong impact on the lowest excitation energy, which can be tuned by almost 1 eV over the diameter range of 2–6 nm. Our calculated excitation energies are about 0.2 eV higher than experimentally measured photoluminescence, and they display the same qualitative size dependence. Focusing on the fine structure of the band-edge excitons, we find that the lowest-lying exciton is spectroscopically dark and about 20–30 meV lower in energy than the higher-lying triplet of the bright states whose degeneracy is slightly broken by crystal field effects.

Data analysis and modeling of small-angle neutron scattering data with contrast variation from bio-macromolecular complexes.

Small-angle neutron scattering (SANS) with contrast variation (CV) is a valuable technique in the structural biology toolchest. Accurate structural parameters-e.g., radii of gyration, volumes, dimensions, and distance distribution(s)-can be derived from the SANS-CV data to yield the shape and disposition of the individual components within stable complexes. Contrast variation is achieved through the substitution of hydrogen isotopes (1H for 2H) in molecules and solvents to alter the neutron scattering properties of each component of a complex. While SANS-CV can be used a stand-alone technique for interrogating the overall structure of biomacromolecules in solution, it also complements other methods such as small-angle X-ray scattering, crystallography, nuclear magnetic resonance, and cryo-electron microscopy. Undertaking a SANS-CV experiment is challenging, due in part to the preparation of significant quantities of monodisperse samples that may require deuterium (2H) labeling. Nevertheless, SANS-CV can be used to study a diverse range biomacromolecular complexes including protein-protein and protein-nucleic acid systems, membrane proteins, and flexible systems resistant to crystallization. This chapter describes how to approach the data analysis and modeling of SANS data, including: (1) Analysis of the forward scattering (I(0)) and calculation of theoretical estimates of contrast; (2) Analysis of the contrast dependence of the radius of gyration using the Stuhrmann plot and parallel axis theorem; (3) Calculation of composite scattering functions to evaluate the size, shape, and dispositions of individual components within a complex, and; (4) Development of real-space models to fit the SANS-CV data using volume-element bead modeling or atomistic rigid body modeling.

Diagnosis of pairing symmetry by vortex and edge spectra in kagome superconductors

Layered kagome metals AV3Sb5 (A=K, Rb, Cs) exhibit diverse correlated electron phenomena. It includes charge density wave formation and superconductivity the pairing symmetry of which, however, is controversial due to contradictory experimental evidence. Through calculations based on real-space lattice models at the mean-field level, we investigate the vortex and surface spectra of all competitive pairing propensities suggested for AV3Sb5 from a weak coupling analysis of unconventional superconductivity. Chiral p-wave pairing emerges as the only option to host Majorana bound states in the vortex core. We find chiral edge states for both p-wave and d-wave pairing, along with flat Andreev surface bound states for f -wave pairing. Our results expand the fingerprint of superconducting pairing, and thus will contribute to resolving the nature of superconductivity in AV3Sb5.

An atomistic approach for the structural and electronic properties of twisted bilayer graphene-boron nitride heterostructures

Twisted bilayer graphene (TBG) has taken the spotlight in the condensed matter community since the discovery of correlated phases. In this work, we study heterostructures of TBG and hexagonal boron nitride (hBN) using an atomistic tight-binding model together with semi-classical molecular dynamics to consider relaxation effects. The hBN substrate has significant effects on the band structure of TBG even in the case where TBG and hBN are not aligned. Specifically, the substrate induces a large mass gap and strong pseudo-magnetic fields that break the layer degeneracy. Interestingly, such degeneracy can be recovered with a second hBN layer. Finally, we develop a continuum model that describes the tight-binding band structure. Our results show that a real-space tight-binding model in combination with semi-classical molecular dynamics is a powerful tool to study the electronic properties of moiré heterostructures, and to explain experimental results in which the effect of the substrate plays an important role.

Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model.

A topological Mott insulator (TMI) with spontaneous time-reversal symmetry breaking and nonzero Chern number has been discovered in a real-space effective model for twisted bilayer graphene (TBG) at 3/4 filling in the strong coupling limit [1]. However, the finite temperature properties of such a TMI state remain illusive. In this work, employing the state-of-the-art thermal tensor network and the perturbative field-theoretical approaches, we obtain the finite-T phase diagram and the dynamical properties of the TBG model. The phase diagram includes the quantum anomalous Hall and charge density wave phases at low T, and an Ising transition separating them from the high-T symmetric phases. Because of the proliferation of excitons-particle-hole bound states-the transitions take place at a significantly reduced temperature than the mean-field estimation. The exciton phase is accompanied with distinctive experimental signatures in such as in charge compressibilities and optical conductivities close to the transition. Our work explains the smearing of the many-electron state topology by proliferating excitons and opens an avenue for controlled many-body investigations on finite-temperature states in the TBG and other quantum moiré systems.

The Laplace-transform embedded discrete fracture model for flow simulation of stimulated reservoir volume

Hydraulic fracturing is a commonly adopted approach to enhance the production of unconventional reservoirs; however, the resulted complex fracture network increases the difficulty in the prediction of the flow behaviors. In this work, for the first time, we propose the Laplace-transform embedded discrete fracture model focusing on the simulation of fluid transport in simulated reservoir volume (SRV). The main hydraulic fracture is represented explicitly by the fracture segments referring to the recently developed simulation scheme, namely the embedded discrete fracture model. The equivalent model and multiple continua model are employed to characterize the fluid flow in SRV. The Laplace-transform finite-different method is used to numerically model the flow among unstimulated reservoir volume, SRV, and main hydraulic fracture with sufficient flexibility to characterize the arbitrary fracture/SRV geometries. As the solution is performed in Laplace domain, the backward Euler difference for time discretization is not necessary. Thus, the stability and convergence problems caused by time discretization are avoided. A series of numerical test cases are discussed to examine the performance of the proposed model. The simulation workflow is validated through the comparison with discrete fracture model and embedded discrete fracture model in real space. It is demonstrated that the proposed Laplace-transform embedded discrete fracture model is accurate for single flow with complex SRV distribution. On the basis of the Laplace-transform embedded discrete fracture model, we provided three applications of the new method: (1) analysis of the SRV effect on fluid flow behavior, (2) pressure transient analysis considering reservoir heterogeneity, (3) production performance analysis with time-varying production rate.

Self-Assembly and Real-Space Modeling in Binary Hard-Particle and Quasicrystalline Systems

Self-Assembly and Real-Space Modeling in Binary Hard-Particle and Quasicrystalline Systems

Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene

We implement a self-consistent Hartree-Fock approximation based on a microscopic model in real space, which allows us to consider the interplay between the Hubbard and the extended Coulomb interaction in twisted bilayer graphene at the magic angle. These two interactions tend to favor different symmetry breaking patterns, having therefore complementary roles in the regimes where one or the other dominates. We show that, for sufficiently large values of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic ground state at the charge neutrality point, while at half-filling of the lowest valence band the state becomes fully spin-polarized. In general, a suitable screening of the extended Coulomb interaction is required to observe the magnetic state in either case, as otherwise the instabilities take place in the charge sector, preferentially in the form of time-reversal, chiral or valley symmetry breaking.

Real-space modeling for complex structures based on small-angle X-ray scattering.

A three-dimensional real-space model has been created for hierarchical materials by matching observed and simulated small-angle X-ray scattering patterns. The simulation is performed by arranging the positions of small primary particles and constructing an aggregate structure in a finite-sized cell. In order to avoid the effect of the finite size of the cell, the cell size is extended to infinity by introducing an asymptotic form of the long-range correlations among the primary particles. As a result, simulations for small-angle X-ray scattering patterns can be performed correctly in the low-wavenumber regime (<0.1 nm-1), allowing the model to handle hundred-nanometre-scale structures composed of primary particles of a few nanometres in size. An aerogel structure was determined using this model, resulting in an excellent match with the experimental scattering pattern. The resultant three-dimensional model can generate cross-sectional images similar to those obtained by transmission electron microscopy, and the calculated pore-size distribution is in accord with that derived from the gas adsorption method.

Decoding the DC and optical conductivities of disordered MoS2 films: an inverse problem

To calculate the conductivity of a material having full knowledge of its composition is a reasonably simple task. To do the same in reverse, i.e. to find information about the composition of a device from its conductivity response alone, is very challenging and even more so in the presence of disorder. An inversion methodology capable of decoding the information contained in the conductivity response of disordered structures has been recently proposed but despite claims of generality and robustness, the method has only been used with 2D systems possessing relatively simple electronic structures. Here we put these claims to the test and generalise the inversion method to the case of monolayer MoS2, a material whose electronic structure is far more complex and elaborate. Starting from the spectral function that describes the DC conductivity of a disordered sample of a single layered MoS2 containing a small concentration of randomly dispersed vacancies, we are able to invert the signal and find the exact composition of defects with an impressive degree of accuracy. Remarkably, equally accurate results are obtained with the optical conductivity. This is indicative of a methodology that is indeed suitable to extract composition information from different 2D materials, regardless of their electronic structure complexity. Calculated conductivity results were used as a proxy for their experimental counterpart and were obtained with an efficient quantum transport code (KITE) based on a real-space multi-orbital tight-binding model with parameters generated by density functional theory.

Processing Aleatory and Epistemic Uncertainties in Experimental Data From Sparse Replicate Tests of Stochastic Systems for Real-Space Model Validation

Abstract This paper presents a practical methodology for propagating and processing uncertainties associated with random measurement and estimation errors (that vary from test-to-test) and systematic measurement and estimation errors (uncertain but similar from test-to-test) in inputs and outputs of replicate tests to characterize response variability of stochastically varying test units. Also treated are test condition control variability from test-to-test and sampling uncertainty due to limited numbers of replicate tests. These aleatory variabilities and epistemic uncertainties result in uncertainty on computed statistics of output response quantities. The methodology was developed in the context of processing experimental data for “real-space” (RS) model validation comparisons against model-predicted statistics and uncertainty thereof. The methodology is flexible and sufficient for many types of experimental and data uncertainty, offering the most extensive data uncertainty quantification (UQ) treatment of any model validation method the authors are aware of. It handles both interval and probabilistic uncertainty descriptions and can be performed with relatively little computational cost through use of simple and effective dimension- and order-adaptive polynomial response surfaces in a Monte Carlo (MC) uncertainty propagation approach. A key feature of the progressively upgraded response surfaces is that they enable estimation of propagation error contributed by the surrogate model. Sensitivity analysis of the relative contributions of the various uncertainty sources to the total uncertainty of statistical estimates is also presented. The methodologies are demonstrated on real experimental validation data involving all the mentioned sources and types of error and uncertainty in five replicate tests of pressure vessels heated and pressurized to failure. Simple spreadsheet procedures are used for all processing operations.

Model DFT exchange holes and the exact exchange hole: Similarities and differences.

Exchange and correlation holes are unique quantum concepts for understanding the nature of electron interactions based on quantum conditional probabilities. Among those, the exact exchange hole is of special interest since it is derived rigorously from first principles without approximations and is often modeled by approximate exchange expressions of density functional theory. In this work, the algorithm for the computation of the spherically averaged exact exchange hole for a given reference point is developed and implemented for molecular orbitals in Gaussian basis functions. The formulas include a novel recursive relation for the spherical average of the Bessel function of the first kind and the asymptotic expressions when the exponential factor of the Bessel function becomes large. This new capability is used to explore the extent to which current popular model exchange holes resemble or differ from the exact exchange hole. Point-wise accuracy of the exchange holes for isolated atoms is important in local hybrid schemes, real-space models of static correlation, and others. We find in this vein that among the models tested here, only the BR89 exchange hole seems more or less suitable for that purpose, while better approximations are still very much on demand. Analyzing the deviations of model exchange holes from the exact exchange hole in molecules such as H2 and Cr2 upon bond stretching reveals new aspects of the left-right static correlation.