Real-space Structure Research Articles

Synthetic Gauge Structures in Real Space in a Ring lattice

Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we propose a way to realize and study gauge structures in real space, manifest in external degrees of freedom of quantum states. We present a model based on a ring-shaped lattice potential, which allows for both Abelian and non-Abelian constructs. Non trivial Wilson loops are shown possible via physical motion of the system. The underlying physics is based on the close analogy of geometric phase with gauge potentials that has been utilized to create synthetic gauge fields with internal states of ultracold atoms. By scaling up to an array with spatially varying parameters, a discrete gauge field can be realized in position space, and its dynamics mapped over macroscopic size and time scales.

Structure retrieval from four-dimensional scanning transmission electron microscopy: Statistical analysis of potential pitfalls in high-dimensional data.

Four-dimensional (4D) scanning transmission electron microscopy is one of the most rapidly growing modes of electron microscopy imaging. The advent of fast pixelated cameras and the associated data infrastructure have greatly accelerated this process. Yet conversion of the 4D datasets into physically meaningful structure images in real space remains an open issue. In this work, we demonstrate that it is possible to systematically create filters that will affect the apparent resolution or even qualitative features of the real-space structure image, reconstructing artificially generated patterns. As initial efforts, we explore statistical model selection algorithms, aiming for robustness and reliability of estimated filters. This statistical model selection analysis demonstrates the need for regularization and cross validation of inversion methods to robustly recover structure from high-dimensional diffraction datasets.

Ab initio electronic structure calculations using a real-space Chebyshev-filtered subspace iteration method

Ab initio electronic structure calculations within Kohn–Sham density functional theory requires a solution for the Kohn–Sham equation. However, the traditional self-consistent field (SCF) approach of solving the equation using iterative diagonalization exhibits an inherent cubic scaling behavior and becomes prohibitive for large systems. The Chebyshev-filtered subspace iteration (CheFSI) method holds considerable promise for large-system calculations by substantially accelerating the SCF procedure. Here, we employed a combination of the real space finite-difference formulation and CheFSI to solve the Kohn–Sham equation, and implemented this approach in ab initio Real-space Electronic Structure (ARES) software in a multi-processor, parallel environment. An improved scheme was proposed to generate the initial subspace of Chebyshev filtering in ARES efficiently, making it suitable for large-scale simulations. The accuracy, stability, and efficiency of the ARES software were illustrated by simulations of large-scale crystalline systems containing thousands of atoms.

Classical mechanics of the Hydrogen atom perturbed by Van der Waals potential interacting with combined electric and magnetic fields

The hydrogen atom perturbed by Van der Waals potential interacting with combined electric and magnetic fields is a non-integrable system, except for some cases, one of which is separable in elliptical coordinates. A detailed study of the classical mechanics of the system is presented giving a complete description of the real phase space structure of the system, we also determine all the generic bifurcations of Liouville tori. This study is supported by numerical investigations via the Poincare surface of section and the phase space trajectories method. The dynamic character of this system depends on the van der Waals potential and the intensity of the magnetic field. Numerical calculations show that if the separability condition is verified, the classical dynamics is regular. However, with a small change in the condition, the dynamic property of the hydrogen atom begins to change. Since the condition is far from integrable behavior, almost all phase space trajectories are chaotic. On the other hand, the intensity of the electric field has no influence on the system.

Local magnetic cluster size identified by neutron total scattering in the site-diluted spin glass SnxFe4−xN (x=0.88)

A detailed structure analysis for the site-diluted $\mathrm{S}{\mathrm{n}}_{x}\mathrm{F}{\mathrm{e}}_{4\ensuremath{-}x}\mathrm{N}$ ($x=0.25$, 0.41, and 0.88) has been carried out through complex modeling of the neutron total scattering data. We present quantitative evidence showing the local ferromagnetic cluster size extending to \ensuremath{\sim}8 \AA{} on average when $\mathrm{S}{\mathrm{n}}_{0.88}\mathrm{F}{\mathrm{e}}_{3.12}\mathrm{N}$ undergoes the spin-glass transition (the other two not showing such a transition). The modeling methodology used in this work involving the corefinement of the nuclear and magnetic structure in both real and reciprocal space can potentially be applied generally to explore a variety of spin-glass material problems.

Flatbands and Perfect Metal in Trilayer Moiré Graphene.

We investigate the electronic structure of a twisted multilayer graphene system forming a moiré pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch states close to the K point in each individual plane. Extending beyond the bilayer case, we show that, when the ratio of the consecutive twist angles is rational, a periodicity emerges in quasimomentum space with moiré Bloch bands even when the system does not exhibit a crystalline lattice structure in real space. For a trilayer geometry, we find flatbands in the spectrum at certain rotation angles. Performing a symmetry analysis of the band model for the trilayer, we prove that the system is a perfect metal in the sense that it is gapless at all energies. This striking result originates from the three Dirac cones which can only gap in pairs and produce bands with an infinite connectivity. It also holds quite generally for multilayer graphene with an odd number of planes under the condition of C_{2z}T symmetry.

Local symmetry theory of resonator structures for the real-space control of edge states in binary aperiodic chains

We propose a real-space approach explaining and controlling the occurrence of edge-localized gap states between the spectral quasibands of binary tight binding chains with deterministic aperiodic long-range order. The framework is applied to the Fibonacci, Thue-Morse and Rudin-Shapiro chains, representing different structural classes. Our approach is based on an analysis of the eigenstates at weak inter-site coupling, where they are shown to generically localize on locally reflection-symmetric substructures which we call local resonators. A perturbation theoretical treatment demonstrates the local symmetries of the eigenstates. Depending on the degree of spatial complexity of the chain, the proposed local resonator picture can be used to predict the occurrence of gap-edge states even for stronger couplings. Moreover, we connect the localization behavior of a given eigenstate to its energy, thus providing a quantitative connection between the real-space structure of the chain and its eigenvalue spectrum. This allows for a deeper understanding, based on local symmetries, of how the energy spectra of binary chains are formed. The insights gained allow for a systematic analysis of aperiodic binary chains and offers a pathway to control structurally induced edge states.

Full real-space analysis of a dodecagonal quasicrystal.

The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki-Gähler tiling. Although the Niizeki-Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.

A semiempirical methodology to characterise a family of microvibration sources

It is well documented that reaction wheels are among the most significant microvibration sources in space applications. These components, despite being nominally identical, can show differences in the generated signals due to manufacturing imperfections in their internal elements, such as ball bearing, internal and external race. In this article a methodology to account for those variations in microvibration predictions is proposed, aiming at generating a disturbance input matrix that encompasses the effects of a family of reaction wheels. With such a tool, it is possible to provide a more accurate microvibration budget at an early stage of the mission, reducing the uncertainty margin usually applied to quantify reaction wheel effects on the structure. As a consequence better designs are produced faster and cheaper. This allows for more flexibility in the mission design and reduces the degree of uncertainties in the predictions. Furthermore, it is shown that the proposed approach is able to characterise the effects of the entire family of wheels by considering only a limited number. The methodology is validated by assessing the microvibration excitation on different structures, including a real space structure with various reaction wheel mounting configurations.

Restoring Real-Space Images of the Structure of Muscle and Other Biological Specimens from Conventional X-Ray Diffraction Patterns

The X-ray diffraction pattern of an object is the Fourier transform of its electron density distribution. Applying an inverse Fourier transformation to the diffraction pattern should in principle result in the restoration of the real-space structure of the object at different magnifications. However, the phase information is lost when the diffraction pattern is recorded on a detector, and the real-space structure is not restored without phase information. This is called the phase problem and has been the greatest obstacle in implementing X-ray diffraction techniques in wide fields. Recently, however, computer-based techniques have been developed to restore the real-space images of objects by recover or preserve phase information. These are collectively called coherent diffractive imaging (CDI). These techniques have been successfully implemented for high-contrast materials such as metal nanoparticles, but they have been less successful for low-contrast biological specimens. Also, it is generally believed that highly coherent X-ray beams are required such as the ones generated by X-ray free electron laser facilities. Here we show the results of implementation of the CDI techniques to diffraction patterns obtained in conventional storage-ring synchrotron radiation facilities. The materials include low-density biological specimens such as muscle and eukaryotic flagella. The successful implementation of the CDI techniques will greatly expand the usefulness of X-ray diffraction techniques.

The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak

The two-dimensional (2D) kinetic theory for a collisionless trapped electron mode is developed based on the Fourier-ballooning transform in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The system consists of two equations: the ballooning (integral) equation with a parameterized Floquet phase and a second order differential equation for the distribution of the Floquet phase. The coupled equations are, then, numerically solved as an eigenvalue problem yielding the 2D mode structure (in real space) as well as the global (phase-independent) eigenvalue for an L-mode parameter set. The 2D mode structure exhibits apparent radial-poloidal asymmetry; due to the poloidal coupling, the radial correlation length is found to be, at least, twice as large as the poloidal one. The global (phase-independent) eigenvalue of the mode differs considerably from the conventional local (phase-dependent) estimate. This paper shares many technical aspects with a published paper that works out the 2D kinetic theory for the ion temperature gradient mode [Xie et al., Phys. Plasmas 24, 102506 (2017)].

Lipid Bilayer Structure Refinement with Saxs/Sans Based Restrained Ensemble Molecular Dynamics

Small angle scattering is a powerful technique that can probe the structure of lipid bilayers on the nanometre scale. Retrieving the real space structure of lipid bilayers from the scattering intensity can be a challenging task, as the fluid nature of lipid bilayers results in a liquid-like scattering pattern which is hard to interpret. The standard approach to this problem is to describe the bilayer structure as a sum of density distributions of separate components of the lipid molecule and then fit the parameters of the distributions against experimental data. The accuracy of the density-based analysis is partially limited by the choice of the functions which are used to describe component distributions, especially in the case of multicomponent bilayers. The number of parameters in the model is balanced by the need for an accurate description of the underlying bilayer structure and the risk of overfitting the data. Here we present an alternative method for the small angle scattering intensity interpretation for lipid bilayers. The method is based on restrained ensemble molecular dynamics simulations, that allow direct incorporation of the scattering data into the simulations in the form of a restraining potential. This approach combines the information that is implicitly contained in the force field used for the simulation with structural data from the scattering intensity and is free from prior assumptions regarding the bilayer structure.

Analysis on Performance of Ferroelectric NC-FETs Based on Real-Space Gibbs-Free Energy With Atomic Channel Structure

Ferroelectric (FE) negative capacitance (NC) MOSFETs is investigated in depth with a full real-space atomic simulator. For the first time, Gibbs-free energy of the whole atomic system is employed to determine the appropriate operation region in polarization-electric-field ( ${P}$ – ${E}$ ) path of the FE layer for FE MOSFETs. With different FE thicknesses, the operation path of the FE layer in MOS structures can be hysteresis or hysteresis-free. For MOSFET structures, the operation path of FE layer will vary with different FE materials. With proper device parameters, the NC effect in FE layer can be obtained with minimum Gibbs-free energy of the MOS and MOSFET structures. The body factor, ${dV}_{G}/{d} \Psi _{S}$ , is obtained with the real-space structure to reflect the influence of the FE layer and optimize the device performance. With the FE layer of the same thickness, the NC-FET with longer channel has a larger body factor which causes the tradeoff between low tunneling current and small body factor. This tradeoff makes it difficult to improve the subthreshold swing by changing the gate length. In addition, the effect of floating metal layer between FE and SiO2 layers in NC-FETs is studied in detail with atomic level real-space analysis for different gate lengths. The metal layer has a stronger influence on the electric characteristics of NC-FETs with longer channel.

Resonant inelastic x-ray incarnation of Young's double-slit experiment.

Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: The elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns, which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural Ir dimers and strong spin-orbit coupling. The double "slits" in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.

Anisotropy effects on the kinetics of colloidal crystallization and melting: comparison of spheres and ellipsoids.

We use alternating current (AC) electric field assisted self-assembly to produce two-dimensional, millimeter scale arrays of ellipsoidal colloids and study the kinetics of their phase reconfiguration by means of confocal microscopy, light scattering, and computer simulation. We find that the kinetics of orientational and positional ordering can be manipulated by changing the shape of the colloids: ellipsoids with aspect ratio 2.0 melt into disordered structures 5.7 times faster compared to spheres. On the other hand, ellipsoids self-assemble into ordered crystals at a similar rate to spheres. Confocal microscopy is used to directly visualize defects in the self-assembled structures. Small-angle light scattering (SALS) quantifies the light diffraction response, which is sensitive to the kinetics of positional and orientational ordering in the self-assembled anisotropic structures. We find three different light diffraction patterns: a phase with high orientational order (with chain-like structure in real space), a phase with high positional and orientational order (characteristic of a close-packed structure), and a phase that is disordered in position but with intermediate orientational order. The large influence of aspect ratio on the kinetics of the positionally and orientationally ordered phase is explored through simulation; it is found that the number of particle degrees of freedom controls the difference between the melting rates of the ellipsoids and spheres. This research contributes to the understanding of reconfiguration kinetics and optical properties of colloidal crystals produced from anisotropic colloids.

Charge-transfer insulation in twisted bilayer graphene

We studied the real space structure of states in twisted bilayer graphene at the `magic angle' $\theta = 1.08^\circ$. The flat bands close to charge neutrality are composed of a mix of `ring' and `center' orbitals around the AA stacking region. An effective model with localized orbitals is constructed, which necessarily includes more than just the four flat bands. Long-range Coulomb interaction causes a charge-transfer at half-filling of the flat bands from the `center' to the `ring' orbitals. Consequently, the Mott phase is a featureless spin-singlet paramagnet. We estimate the effective Heisenberg coupling that favors the singlet coupling to be $J = 3.3$ K, consistent with experimental values. The superconducting state depends on the nature of the dopants: hole-doping yields $p+ip$-wave whereas electron-doping yields $d+id$-wave pairing symmetry.

Real-time coherent diffraction inversion using deep generative networks

Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging (CDI). Typical phase retrieval algorithms are iterative in nature, and hence, are time-consuming and computationally expensive, making real-time imaging a challenge. Furthermore, iterative phase retrieval algorithms struggle to converge to the correct solution especially in the presence of strong phase structures. In this work, we demonstrate the training and testing of CDI NN, a pair of deep deconvolutional networks trained to predict structure and phase in real space of a 2D object from its corresponding far-field diffraction intensities alone. Once trained, CDI NN can invert a diffraction pattern to an image within a few milliseconds of compute time on a standard desktop machine, opening the door to real-time imaging.

Reservoir engineering of bosonic lattices using chiral symmetry and localized dissipation

We show how a generalized kind of chiral symmetry can be used to construct highly efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension and does not rely on translational invariance. We show how the relevant symmetry operation directly determines the real-space correlation structure in the steady state and give several examples that are within reach in several one- and two-dimensional quantum photonic platforms.

Discrete discontinuous basis projection method for large-scale electronic structure calculations.

We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient, systematically improvable, discontinuous basis spanning the occupied subspace and project the real-space Hamiltonian onto the span. In calculations on a range of systems, we find that accurate energies and forces are obtained with 8-25 basis functions per atom, reducing the dimension of the associated real-space eigenproblems by 1-3 orders of magnitude.

Mesoscopic real-space structures in spin-glass aging: The Edwards-Anderson model

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below $T_{\rm c}$ and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures $T$ can be collapsed by scaling them with $T^{1.75}$, a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the cluster, as recently assumed in a coarse grained model of dense colloidal dynamics. The evolving structure of clusters in real space is finally sssociated to the decay of the thermo-remanent magnetization. Our analysis provides an unconventional coarse-grained description of spin glass aging as statistically subordinated to a Poisson quaking process and highlights record dynamics as a viable common theoretical framework for aging in different systems.