Real-space Structure Research Articles

Spin relaxation in wurtzite nanowires

We theoretically investigate the D'yakonov-Perel' spin-relaxation properties in diffusive wurtzite semiconductor nanowires and their impact on the quantum correction to the conductivity. Although the lifetime of the long-lived spin states is limited by the dominant $k$-linear spin-orbit contributions in the bulk, these terms show almost no effect in the finite-size nanowires. Here, the spin lifetime is essentially determined by the small $k$-cubic spin-orbit terms and nearly independent of the wire radius. At the same time, these states possess in general a complex helical structure in real space that is modulated by the spin-precession length induced by the $k$-linear terms. For this reason, the experimentally detected spin relaxation largely depends on the ratio between the nanowire radius and the spin-precession length as well as the type of measurement. In particular, it is shown that while a variation of the radius hardly affects the magnetoconductance correction, which is governed by the long-lived spin states, the change in the spin lifetime observed in optical experiments can be dramatic. We compare our results with recent experimental studies on wurtzite InAs nanowires.

Density Functional Theory under the Bubbles and Cube Numerical Framework.

Density functional theory within the Kohn–Sham density functional theory (KS-DFT) ansatz has been implemented into our bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional (1D) numerical grids multiplied with spherical harmonics (bubbles). The remainder, i.e., the cube, which is the cusp-free and smooth difference between the atomic one-center contributions and the exact molecular function, is represented on a three-dimensional (3D) equidistant grid by using a tractable number of grid points. The implementation of the methods is demonstrated by performing 3D numerical KS-DFT calculations on light atoms and small molecules. The accuracy is assessed by comparing the obtained energies with the best available reference energies.

Stabilization of Polar Nanoregions in Pb-free Ferroelectrics.

The formation of polar nanoregions through solid-solution additions is known to enhance significantly the functional properties of ferroelectric materials. Despite considerable progress in characterizing the microscopic behavior of polar nanoregions (PNR), understanding their real-space atomic structure and dynamics of their formation remains a considerable challenge. Here, using the method of dynamic pair distribution function, we provide direct insights into the role of solid-solution additions towards the stabilization of polar nanoregions in the Pb-free ferroelectric of Ba(Zr,Ti)O_{3}. It is shown that for an optimum level of substitution of Ti by larger Zr ions, the dynamics of atomic displacements for ferroelectric polarization are slowed sufficiently below THz frequencies, which leads to increased local correlation among dipoles within PNRs. The dynamic pair distribution function technique demonstrates a unique capability to obtain insights into locally correlated atomic dynamics in disordered materials, including new Pb-free ferroelectrics, which is necessary to understand and control their functional properties.

FRACTAL FEATURES OF THE QUANTIZED SCANNING TUNNELING CURRENT AND THE LOCAL DENSITY OF STATES FOR A QUANTUM CORRAL

We found that quantization of the scanning tunneling microscope (STM) current becomes apparent as the size of a quantum corral (QC) decreases and the corral thickness increases. It is shown that STM current images provide the position dependence of the conduction channels and local density of states (LDOS) images provide the spatial distribution of differential conductance channels. We clarified for the first time that there exist fractal structures in the QC size dependence of the [Formula: see text]–[Formula: see text] characteristic and in that of the LDOS. LDOS images also exhibit a fractal structure as a function of bias voltage. These results demonstrate fractal structures in energy space and real space. For an extremely large QC, we found that the [Formula: see text]–[Formula: see text] curve becomes Ohmic and the LDOS converges to a constant corresponding to the bulk two-dimensional density of states.

Revealing the correlation between real-space structure and chiral magnetic order at the atomic scale

We image simultaneously the geometric, electronic and magnetic structure of a buckled iron bilayer film that exhibits chiral magnetic order. We achieve this by combining spin-polarized scanning tunneling microscopy and magnetic exchange force microscopy (SPEX), to independently characterize the geometric as well as the electronic and magnetic structure of non-flat surfaces. This new SPEX imaging technique reveals the geometric height corrugation of the reconstruction lines resulting from strong strain relaxation in the bilayer, enabling the decomposition of the real-space from the eletronic structure at the atomic level, and the correlation with the resultant spin spiral ground state. By additionally utilizing adatom manipulation, we reveal the chiral magnetic ground state of portions of the unit cell that were not previously imaged with SP-STM alone. Using density functional theory (DFT), we investigate the structural and electronic properties of the reconstructed bilayer and identify the favorable stoichiometry regime in agreement with our experimental result.

Extended hierarchical solvent perturbations from curved surfaces of mesoporous silica particles in a deep eutectic solvent

HypothesisMany applications of deep eutectic solvents (DES) rely on exploitation of their unique yet complex liquid structures. Due to the ionic nature of the DES components, their diffuse structures are perturbed in the presence of a charged surface. We hypothesize that it is possible to perturb the bulk DES structure far (>100 nm) from a curved, charged surface with mesoscopic dimensions. ExperimentsWe performed in situ, synchrotron-based ultra-small angle X-ray scattering (USAXS) experiments to study the solvent distribution near the surface of charged mesoporous silica particles (MPS) (≈0.5 µm in diameter) suspended in both water and a common type of DES (1:2 choline Cl-:ethylene glycol). FindingsA careful USAXS analysis reveals that the perturbation of electron density distribution within the DES extends ≈1 μm beyond the particle surface, and that this perturbation can be manipulated by the addition of salt ions (AgCl). The concentration of the pore-filling fluid is greatly reduced in the DES. Notably, we extracted the real-space structures of these fluctuations from the USAXS data using a simulated annealing approach that does not require a priori knowledge about the scattering form factor, and can be generalized to a wide range of complex small-angle scattering problems.

Topological antiferromagnetic spintronics

The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field that is exploring the links between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topological superconductors, to control topological protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.

Atomic resolution on the (111)B surface of mercury cadmium telluride by scanning tunneling microscopy

The real-space atomic surface structure of mercury cadmium telluride was successfully achieved on the $(111)B$ surface of $\mathrm{H}{\mathrm{g}}_{0.78}\mathrm{C}{\mathrm{d}}_{0.22}\mathrm{Te}$ by ultrahigh-vacuum scanning tunneling microscopy (STM). The work casts light on the reconstructions of the $(111)B$ surface unraveling a $(2\ifmmode\times\else\texttimes\fi{}2)$ surface reconstruction induced by adatom adsorption of Cd. The other $(2\ifmmode\times\else\texttimes\fi{}2)$ surface reconstruction is clarified to be induced by the single Te vacancy, which is more stable than the reconstruction of multivacancies in contrast to the prevailing view. The simulated STM images are in good agreement with the experiments. We also observed an in situ morphology transition from the $(1\ifmmode\times\else\texttimes\fi{}1)$ structure to those $(2\ifmmode\times\else\texttimes\fi{}2)$ reconstructions, implying the stability of the reconstructions.

Optimizing self-consistent field theory block copolymer models with X-ray metrology.

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

High-resolution imaging of silicene on an Ag(111) surface by atomic force microscopy

Silicene, a two-dimensional (2D) honeycomb arrangement of Si atoms, is expected to have better electronic properties than graphene and has been mostly synthesized on Ag surfaces. Although scanning tunneling microscopy (STM) has been used for visualizing its atomic structure in real space, the interpretation of STM contrast is not straightforward and only the topmost Si atoms were observed on the $(4\ifmmode\times\else\texttimes\fi{}4)$ silicene/Ag(111) surface. Here, we demonstrate that high-resolution atomic force microscopy (AFM) can resolve all constituent Si atoms in the buckled honeycomb arrangement of the $(4\ifmmode\times\else\texttimes\fi{}4)$ silicene. Site-specific force spectroscopy attributes the origin of the high-resolution AFM images to chemical bonds between the AFM probe apex and the individual Si atoms on the $(4\ifmmode\times\else\texttimes\fi{}4)$ silicene. A detailed analysis of the geometric parameters suggests that the pulling up of lower-buckled Si atoms by the AFM tip could be a key for high-resolution AFM, implying a weakening of the Si-Ag interactions at the interface. We expect that high-resolution AFM will also unveil atomic structures of edges and defects of silicene, or other emerging 2D materials.

Theoretical study on Pb2VO2F5: large birefringence derived from optical anisotropies of VO2F4 groups

The Pb2VO2F5 crystal was synthesized by hydrothermal method. The crystal structure consists of tetranuclear [Pb4O6F22] and twinborn V2O4F6 units, which share the O and F atoms forming a three-dimensional framework. The birefringence of the compound was investigated using the first principles. The calculations results show that the compound has a large birefringence of 0.336 at 1064 nm. Researches indicate that its large birefringence originates mainly from the distorted VO2F4 groups based on the real-space atom-cutting method and structure–property relationships analysis. Furthermore, the IR spectrum, thermal behaviors, and UV–Vis–IR diffuse reflectance spectroscopy of the compound are also presented.

On static triplet structures in fluids with quantum behavior.

The problem of the equilibrium triplet structures in fluids with quantum behavior is discussed. Theoretical questions of interest to the real space structures are addressed by studying the three types of structures that can be determined via path integrals (instantaneous, centroid, and total thermalized-continuous linear response). The cases of liquid para-H2 and liquid neon on their crystallization lines are examined with path-integral Monte Carlo simulations, the focus being on the instantaneous and the centroid triplet functions (equilateral and isosceles configurations). To analyze the results further, two standard closures, Kirkwood superposition and Jackson-Feenberg convolution, are utilized. In addition, some pilot calculations with path integrals and closures of the instantaneous triplet structure factor of liquid para-H2 are also carried out for the equilateral components. Triplet structural regularities connected to the pair radial structures are identified, a remarkable usefulness of the closures employed is observed (e.g., triplet spatial functions for medium-long distances, triplet structure factors for medium k wave numbers), and physical insight into the role of pair correlations near quantum crystallization is gained.

In Silico Synthesis of Microgel Particles.

Microgels are colloidal-scale particles individually made of cross-linked polymer networks that can swell and deswell in response to external stimuli, such as changes to temperature or pH. Despite a large amount of experimental activities on microgels, a proper theoretical description based on individual particle properties is still missing due to the complexity of the particles. To go one step further, here we propose a novel methodology to assemble realistic microgel particles in silico. We exploit the self-assembly of a binary mixture composed of tetravalent (cross-linkers) and bivalent (monomer beads) patchy particles under spherical confinement in order to produce fully bonded networks. The resulting structure is then used to generate the initial microgel configuration, which is subsequently simulated with a bead–spring model complemented by a temperature-induced hydrophobic attraction. To validate our assembly protocol, we focus on a small microgel test case and show that we can reproduce the experimental swelling curve by appropriately tuning the confining sphere radius, something that would not be possible with less sophisticated assembly methodologies, e.g., in the case of networks generated from an underlying crystal structure. We further investigate the structure (in reciprocal and real space) and the swelling curves of microgels as a function of temperature, finding that our results are well described by the widely used fuzzy sphere model. This is a first step toward a realistic modeling of microgel particles, which will pave the way for a careful assessment of their elastic properties and effective interactions.

Self-assembled monolayers of sulfonate-terminated alkanethiols investigated by frequency modulation atomic force microscopy in liquid

A molecular-scale understanding of self-assembled monolayers (SAMs) of sulfonate-terminated alkanethiols is crucial for interfacial studies of functionalized SAMs and their various applications. However, such an understanding has been difficult to achieve because of the lack of direct information on these molecular-scale structures in real space. In this study, we investigated the structures of sulfonate SAMs of sodium 11-mercapto-1-undecanesulfonate (MUS) by frequency modulation atomic force microscopy (FM-AFM) in liquid. The subnanometer-resolution FM-AFM images showed that the single-component MUS SAM prepared in pure water had random surface structures. In contrast, the MUS SAM prepared in a water–ethanol mixed solvent showed periodic striped structures with a flat-lying conformation. The results suggest a significant solvent effect on molecular-scale structures of long-chain sulfonate SAMs. In addition, we investigated the molecular-scale structures of mixed SAMs of MUS and 11-mercapto-1-undecanol (MUO) with alkane chains of the same length. The FM-AFM images of the mixed SAMs showed clear phase separation between MUS SAM and MUO SAM domains. In the MUO SAM domains, the incorporated MUS molecules appeared as protrusions. The results obtained in this study provide direct structural information on long-chain sulfonate and mixed SAMs.

Electric field driven evolution of topological domain structure in hexagonal manganites

Controlling and manipulating the topological state represents an important topic in condensed matters for both fundamental researches and applications. In this work, we focus on the evolution of a real-space topological domain structure in hexagonal manganites driven by electric field, using the analytical and numerical calculations based on the Ginzburg-Landau theory. It is revealed that the electric field drives a transition of the topological domain structure from the type-I pattern to the type-II one. In particular, it is identified that a high electric field can enforce the two antiphase-plus-ferroelectric ($\mathrm{AP}+\mathrm{FE}$) domain walls with $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Phi}}=\ensuremath{\pi}/3$ to approach each other and to merge into one domain wall with $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Phi}}=2\ensuremath{\pi}/3$ eventually if the electric field is sufficiently high, where $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Phi}}$ is the difference in the trimerization phase between two neighboring domains. Our simulations also reveal that the vortex cores of the topological structure can be disabled at a sufficiently high critical electric field by suppressing the structural trimerization therein, beyond which the vortex core region is replaced by a single ferroelectric domain without structural trimerization ($Q=0$). Our results provide a stimulating reference for understanding the manipulation of real-space topological domain structure in hexagonal manganites.

PRISM Theory Study of Amphiphilic Block Copolymer Solutions with Varying Copolymer Sequence and Composition

We present a comparison of Polymer Reference Interaction Site Model (PRISM) theory and molecular dynamics (MD) simulations for studying amphiphilic block copolymers in solution. We use a generic coarse-grained model to represent amphiphilic A–B block copolymers in implicit solvent with the solvophobicity of the B segments captured using effective B–B pairwise attraction modeled using the Lennard-Jones potential. We study the assembly of the amphiphilic A–B block copolymer as a function of solvophobicity for varying copolymer sequences (diblock and triblock) and composition (solvophobic-rich or solvophilic-rich). The PRISM theory equation along with the atomic Percus–Yevick closure is solved to obtain the intermolecular pair correlations in real space, g(r), and structure factors in Fourier space, S(k), for block copolymer solutions at increasing values of solvophobicity. The real-space intermolecular pair correlation functions and structure factors from PRISM theory and from MD simulations are compared di...

Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures

We investigated the structure of SiO2 glass up to 172 GPa using high-energy X-ray diffraction. The combination of a multichannel collimator with diamond anvil cells enabled the measurement of structural changes in silica glass with total X-ray diffraction to previously unachievable pressures. We show that SiO2 first undergoes a change in Si-O coordination number from fourfold to sixfold between 15 and 50 GPa, in agreement with previous investigations. Above 50 GPa, the estimated coordination number continuously increases from 6 to 6.8 at 172 GPa. Si-O bond length shows first an increase due to the fourfold to sixfold coordination change and then a smaller linear decrease up to 172 GPa. We reconcile the changes in relation to the oxygen-packing fraction, showing that oxygen packing decreases at ultrahigh pressures to accommodate the higher than sixfold Si-O coordination. These results give experimental insight into the structural changes of silicate glasses as analogue materials for silicate melts at ultrahigh pressures.

Relativistic response and novel spin-charge plasmon at the Tl/Si(111) surface

We present a comprehensive \textit{ab initio} analysis of the spin-charge correlations at the Tl/Si(111) surface, where the spin-orbit interaction is so strong that a detailed treatment of the non-collinear electron spin appears decisive for the correct description of the response properties. The relativistic limit enforces a unified treatment of the spin and charge densities as a four-vector, and the response function acquires then a 4$\times$4 tensor structure. Our all-electron implementation allows to resolve the real space structure of the possible collective modes, and demonstrates the emergence of a novel collective excitation combining transverse-spin and ordinary charge oscillations of a similar order of magnitude, whose spin character is strongly enhanced as we approach the $q$$\rightarrow$0 momentum limit.

Imaging the real space structure of the spin fluctuations in an iron-based superconductor

Spin fluctuations are a leading candidate for the pairing mechanism in high temperature superconductors, supported by the common appearance of a distinct resonance in the spin susceptibility across the cuprates, iron-based superconductors and many heavy fermion materials. The information we have about the spin resonance comes almost exclusively from neutron scattering. Here we demonstrate that by using low-temperature scanning tunnelling microscopy and spectroscopy we can characterize the spin resonance in real space. We show that inelastic tunnelling leads to the characteristic dip-hump feature seen in tunnelling spectra in high temperature superconductors and that this feature arises from excitations of the spin fluctuations. Spatial mapping of this feature near defects allows us to probe non-local properties of the spin susceptibility and to image its real space structure.

Design of Non-Deterministic Quasi-random Nanophotonic Structures Using Fourier Space Representations

Despite their seemingly random appearances in the real space, quasi-random nanophotonic structures exhibit distinct structural correlations and have been widely utilized for effective photon management. However, current design approaches mainly rely on the deterministic representations consisting two-dimensional (2D) discretized patterns in the real space. They fail to capture the inherent non-deterministic characteristic of the quasi-random structures and inevitably result in a large design dimensionality. Here, we report a new design approach that employs the one-dimensional (1D) spectral density function (SDF) as the unique representation of non-deterministic quasi-random structures in the Fourier space with greatly reduced design dimensionality. One 1D SDF representation can be used to generate infinite sets of real space structures in 2D with equally optimized performance, which was further validated experimentally using light-trapping structures in a thin film absorber as a model system. The optimized non-deterministic quasi-random nanostructures improve the broadband absorption by 225% over the unpatterned cell.