2-fold Symmetry Research Articles

Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems

The incommensurate ${30}^{\ensuremath{\circ}}$ twisted bilayer graphene (BG) possesses both relativistic Dirac fermions and quasiperiodicity with 12-fold rotational symmetry arising from the interlayer interaction [Ahn et al., Science 361, 782 (2018) and Yao et al., Proc. Natl. Acad. Sci. USA 115, 6928 (2018)]. Understanding how the interlayer states interact with each other is of vital importance for identifying and subsequently engineering the quasicrystalline order in the layered structure. Herein, via symmetry and group representation theory we unravel the interlayer hybridization selection rules governing the interlayer coupling in both untwisted and twisted BG systems. Compared with the only allowed equivalent hybridization in ${D}_{6h}$ untwisted BG, ${D}_{6}$ twisted BG permits equivalent and mixed hybridizations, and ${D}_{6d}$ graphene quasicrystal allows both equivalent and nonequivalent hybridizations. The energy-dependent hybridization strengths in graphene quasicrystal and ${D}_{6}$ twisted BG show two remarkable characteristics: (i) near the Fermi level the weak hybridization owing to the relatively large energy difference between Dirac bands from top and bottom layers, and (ii) in high-energy regions the electron-hole asymmetry of hybridization strength with stronger interlayer coupling for holes, which arises from the non-nearest-neighbor interlayer hoppings and the wave-function phase difference between pairing states. These hybridization-generated band structures and their hybridization strength characteristics are verified by the calculated optical conductivity spectra. Our theoretical study paves a way for revealing the interlayer hybridization in van der Waals layered systems.

Epitaxial Growth of Metals on (100) SrTiO3: The Influence of Lattice Mismatch and Reactivity

Abstract The model system Me/(100) SrTiO3 (Me: Pd, Pt, Cu, Ni, Cr, Mo, Nb, and Al) was used to show that there exists a simple correlation between the formation of particular epitaxial orientations, the lattice mismatch between metal and SrTiO3, and the oxygen affinity of the metal. The growth of the metal films on the (100) SrTiO3 surface was studied by reflection high-energy electron diffraction. Most metals (Pd, Pt, Ni, Nb and Al) grew with the following epitaxial orientation relationship on the SrTiO3: (100) SrTiO3 | | (100) Me, [001] SrTiO3 | | [001] Me. A second epitaxial orientation relationship was detected for Cr and Mo: (100) SrTiO3 | | (100) Cr, Mo, [001] SrTiO3 | | [011] Cr, Mo. For Mo, this orientation was detected only at very high growth temperatures. For each of the epitaxial orientation relationships, the substrate and film planes of four fold symmetry were parallel. Besides the second epitaxial orientation relationship, a third epitaxial orientation relationship was detected for Mo at growth temperatures below 900 K: (100) SrTiO3 | | (110) Mo, [001] SrTiO3 | | [001] Mo. In contrast to all other metals under investigation, Cu grew with a (111) fiber texture on the (100) SrTiO3 surface. The appearance of the first two epitaxial orientation relationships can be interpreted with a simple relationship between the metals’ oxygen affinities and the lattice mismatches with SrTiO3. This relationship can be used for other metals to predict epitaxy on the (100) SrTiO3 surface.

Epitaxial Ferrimagnetic Mn4N Thin Films on GaN by Molecular Beam Epitaxy

Direct epitaxial integration of magnetic layers with wide bandgap nitride semiconductors will enable spin-controlled transport and photonic phenomena, seeding ideas for functional spintronic devices. Using plasma-assisted molecular beam epitaxy (MBE) in a previously unexplored window, significantly improved ferrimagnetic Mn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> N layers are successfully grown on GaN with ~1 nm surface roughness. Distinct from earlier reports, the Mn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> N layers grown on GaN are found to be [001] oriented with 12-fold in-plane symmetry in the diffraction pattern. This unique epitaxial registry originates from three equivalent rotational domains. The ferrimagnetic magnetotransport properties of low growth temperature Mn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> N layers on GaN are comparable to those reported on cubic substrates such as MgO. However, a sign-flip of the Hall resistance is discovered for Mn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> N layers grown above 300 °C.

Synthesis of Oriented Hexasomes and Asymmetric Nucleosomes Using a Template Editing Process.

Nucleosomes, the structural building blocks of chromatin, possess 2-fold pseudo symmetry which can be broken through differential modification or removal of one copy of a pair of sister histones. The resultant asymmetric nucleosomes and hexasomes have been implicated in gene regulation, yet the use of these noncanonical substrates in chromatin biochemistry is limited, owing to the lack of efficient methods for their preparation. Here, we report a strategy that allows the orientation of these asymmetric species to be tightly controlled relative to the underlying DNA sequence. Our approach is based on the use of truncated DNA templates to assemble oriented hexasomes followed by DNA ligation and, in the case of asymmetric nucleosomes, addition of the missing heterotypic histones. We show that this approach is compatible with multiple nucleosome positioning sequences, allowing the generation of desymmetrized mononucleosomes and oligonucleosomes with varied DNA overhangs and heterotypic histone H2A/H2B dimer compositions. Using this technology, we examine the functional consequences of asymmetry on BRG1/BRM associated factor (BAF) complex-mediated chromatin remodeling. Our results indicate that cancer-associated histone mutations can reprogram the inherent activity of BAF chromatin remodeling to induce aberrant chromatin structure.

Cohomology groups for spaces of 12-fold tilings

We consider tilings of the plane with 12-fold symmetry obtained by the cut and projection method. We compute their cohomology groups using the techniques introduced in [5]. To do this we completely describe the window, the orbits of lines under the group action and the orbits of 0-singularities. The complete family of generalized 12-fold tilings can be described using 2-parameters and it presents a surprisingly rich cohomological structure. To put this finding into perspective, one should compare our results with the cohomology of the generalized 5-fold tilings (more commonly known as generalized Penrose tilings). In this case the tilings form a 1-parameter family, which fits in simply one of two types of cohomology.

Subahnale dan Rang-rang Pembelajaran Matematika SMP

The purpose of this research is to find mathematical concepts in the cultural heritage of songket cloth and how to apply them as a medium for learning mathematics in junior high schools. The results of this study can be used as a reference for junior high school teachers to choose culture-based learning media related to student life, especially in Lombok. This research is an ethnomathematical research with the research method used is a qualitative research method with an ethnographic approach. The research was conducted in September, October, and November 2021 in Sukarara village, Lombok, West Nusa Tenggara. The subjects in this study were craft works in the form of songket cloth and songket weavers who were active in the village of Sukarara which consisted of three weavers. Data were collected by documentation, document observation, and interviews. The documents obtained were then analyzed related to the content of the mathematical concepts contained therein. The conclusion of this study is that the quality of mathematics learning can be improved by using the traditional songket subahnale cloth as a medium or learning aid. Some mathematical concepts that can be learned with songket subahnale as the medium are congruence, similarity, perimeter of flat shapes, area of flat shapes, folding symmetry, comparisons, pattern tracing. Songket fabrics that can be used as media are songket subahnale woven fabrics with geometric motifs such as diamond motifs, rang-rang motifs, and hexagons

A novel photonic quasi-crystal fiber for transmission of orbital angular momentum modes

A photonic quasi-crystal fiber (PQF) based on the 12-fold symmetry quasi-periodic structure is designed for transmission of orbital angular momentum (OAM) modes. In this PQF, the effective refractive index difference of the degenerate modes is greater than 10−4 and 110 high-quality OAM modes in the wavelength range between 1.46 and 1.60 µm are supported. The characteristics of the PQF are numerically analyzed by the finite element method. This PQF with a confinement loss of less than 10−9 dB/m and effective mode area larger than 100 µm2 has many potential applications in mode division multiplexing for fiber communication systems.

Geometrical meaning of statistical isotropy of smooth random fields in two dimensions

We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, ${\mathcal{W}}_{1}$, as our basic tool we first examine geometrical properties of single structures. For simple closed curves in two dimensions we show that ${\mathcal{W}}_{1}$ is proportional to the identity matrix if the curve has $m$-fold symmetry, with $m\ensuremath{\ge}3$. Then we elaborate on how ${\mathcal{W}}_{1}$ maps any arbitrary shaped simple closed curve to an ellipse that is unique up to translations of its centroid. We also carry out a comparison of the shape parameters, $\ensuremath{\alpha}$ and $\ensuremath{\beta}$, defined using ${\mathcal{W}}_{1}$, with the filamentarity parameter defined using two scalar Minkowski functionals---area and contour length. We show that they contain complementary shape information, with ${\mathcal{W}}_{1}$ containing additional information of orientation of structures. Next, we apply our method to boundaries of excursion sets of random fields and examine what statistical isotropy means for the geometry of the excursion sets. Focusing on Gaussian isotropic fields, and using a seminumerical approach we quantify the effect of finite sampling of the field on the geometry of the excursion sets. In doing so we obtain an analytic expression for $\ensuremath{\alpha}$ which takes into account the effect of finite sampling. Finally we derive an analytic expression for the ensemble expectation of ${\mathcal{W}}_{1}$ for Gaussian anisotropic random fields. Our results provide insights that are useful for designing tests of statistical isotropy using cosmological data.

Effect of graphene domains orientation on quasi van der Waals epitaxy of GaN

We demonstrate the growth features of III-nitrides on graphene buffer layers obtained by the CVD method on a copper catalyst with different dominant grain orientations. The reflection high-energy electron diffraction technique (RHEED) is used to map the 2D reciprocal space structures of graphene buffers and growing nitride layers. The RHEED reciprocal space pattern for the graphene layer grown on a (111) textured copper foil and transferred to a SiO2/Si substrate demonstrates the sixfold symmetry characteristic of a highly oriented material. In turn, graphene grown on a Cu (100) foil consists of two types of domains that are 30° rotated relative to each other. It has also been demonstrated that III-nitride films exactly repeat the texture of the 2D graphene buffers. The GaN sample grown over the highly textured substrate demonstrates a clear sixfold symmetry of the RHEED reciprocal space map as well as {101¯3} XRD pole figure, which is close to 2D surface morphology. In turn, the GaN film grown over the graphene buffer layer transferred from the Cu (100) textured foil has 12-fold axial symmetry, which is equivalent to the essentially two-domain in-plane orientation of the initial graphene.

Van der Waals Superstructure and Twisting in Self-Intercalated Magnet with Near Room-Temperature Perpendicular Ferromagnetism.

The emergence of van der Waals (vdW) magnets has created unprecedented opportunities to manipulate magnetism for advanced spintronics based upon all-vdW heterostructures. Among various vdW magnets, Cr1+δTe2 possesses high temperature ferromagnetism along with possible topological spin textures. As this system can support self-intercalation in the vdW gap, it is crucial to precisely pinpoint the exact intercalation to understand the intrinsic magnetism of the system. Here, we developed an iterative method to determine the self-intercalated structures and show evidence of vdW "superstructures" in individual Cr1+δTe2 nanoplates exhibiting magnetic behaviors distinct from bulk chromium tellurides. Among 26,332 possible configurations, we unambiguously identified the Cr-intercalated structure as 3-fold symmetry broken Cr1.5Te2 segmented by vdW gaps. Moreover, a twisted Cr-intercalated layered structure is observed. The spontaneous formation of twisted vdW "superstructures" not only provides insight into the diverse magnetic properties of intercalated vdW magnets but may also add complementary building blocks to vdW-based spintronics.

Dynamical properties of lithium borohydride – ammine composite LiBH4·NH3: A nuclear magnetic resonance study

The lithium borohydride – ammine composite LiBH4·NH3 exhibits a high hydrogen density and combines [BH4]− anions and neutral NH3 molecules within the common crystal structure. To study the dynamical properties of this compound, we have measured the 1H, 11B, and 7Li nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates over the temperature range of 18 – 293 K. Our measurements have revealed a coexistence of four types of BH4 reorientational jump processes with different activation energies. One of these processes corresponds to extremely fast BH4 reorientations with the jump rate reaching ~108 s−1 already at 95 K; this fast process is characterized by the activation energy of 78(2) meV. The local coordination of [BH4]− anions in LiBH4·NH3 suggests that the fastest process is represented by rotations around a single 3-fold symmetry axis of the BH4 tetrahedron. The slower processes characterized by the activation energies of 152(5) meV, 216(7) meV, and 297(10) meV may be attributed to reorientations around other symmetry axes of the BH4 tetrahedron. In the studied temperature range up to 293 K, we have not found any signs of diffusive Li+ jumps in LiBH4·NH3 at the frequency scale of ~104 s−1 or higher.

Heterogeneous design and mechanical analysis of HELIAS 5‐B helium‐cooled pebble bed breeding blanket concept

One of the most challenging objectives of the European research concerning nuclear fusion technology, promoted by the EUROfusion consortium, is to bring stellarator-type nuclear fusion devices to maturity. To this purpose, studies on a large HELIcal-axis advanced stellarator (HELIAS), extrapolated from Wendelstein 7-X and based on a 5-fold symmetry (HELIAS 5-B), are currently ongoing. The HELIAS 5-B stellarator reactor will be endowed with a breeding blanket (BB) system to allow for the self-sustainability of the nuclear fusion reaction and make it suitable for electricity generation. In this paper, we present the first ever heterogeneous mechanical design and the preliminary structural assessment of a bean-shaped ring of a HELIAS 5-B BB sector. The proposed mechanical design, which is based on the helium-cooled pebble bed (HCPB) BB concept and developed according to the “sandwich” architecture, foresees an actively cooled segment box connected to a back-supporting structure equipped with manifolds. The internal region (breeding zone) is reinforced by actively cooled steel plates. The proposed heterogeneous design was checked against nominal loads and an in-box loss of coolant accidental scenario, which is a typical design driver for BBs. The assessment has been performed according to the RCC-MRx structural design code. Our results are herewith presented and critically discussed, focusing on the potential follow-up of the HELIAS 5-B HCPB BB design.

Synthesis, crystal structure and antimicrobial activity of a new polymeric copper(II) complex derived from N'-(pyridin-2-ylmethylene)isonicotinohydrazide

A new polymeric copper(II) complex [Cu3L3(μ3-NO3)]n·2nNO3, derived from the Schiff base ligand N'-(pyridin-2-ylmethylene)isonicotinohydrazide (HL) with copper nitrate in methanol, was prepared and characterized by elemental analysis, IR and UV-Vis spectra. The structure of the complex was further confirmed by single crystal X-ray diffraction technique. The Schiff base ligand coordinates to the Cu atoms through the phenolate O, imino O, and two pyridine N atoms. The Cu atom is in a square pyramidal coordination, with the three chelate donor atoms of the Schiff base ligand and the terminal nitrogen donor atom of a symmetry related Schiff base ligand defining the basal plane, and with one oxygen atom of the coordinated nitrate ligand at the apical position. The nitrate ligand bridges three [CuL] units with a crystallographic three fold rotation axis symmetry. The effect of the complex on the antimicrobial activity against Staphylococcus aureus, Escherichia coli, and Candida albicans was studied.

Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate.

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with l-fold symmetry, ranging from quadrupole (l=2) to heptagon modes (l=7), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the l=6 mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.

Revisit of the structure of Ω precipitate in Al-Cu-Mg-Ag alloys

Re-examination of the structure of Ω precipitate in Al-Cu-Mg-Ag alloys through first-principles density functional theory (DFT) calculation reveals that the widely-accepted orthorhombic structure of the ‘metastable’ Ω phase is actually tetragonal that is identical to that of the equilibrium θ phase in binary Al-Cu alloys. When the tetragonal θ (i.e. Ω) is embedded in α-Al matrix as thin plates, the elastic distortion imposed by the surrounding α-Al matrix can reduce the original 4-fold symmetry of the tetragonal structure to the 2-fold symmetry of the orthorhombic structure. The DFT calculation results also indicate that the presence of Mg and Ag at the θ/α-Al interface can dramatically facilitate the θ formation. The clarification of the Ω structure and the role of Mg and Ag in θ formation provides insights into how to facilitate precipitation of an intrinsically strong equilibrium phase as a key strengthening constituent in the microstructure.

3× Axial vs 3× Equatorial: The ΔGGA Value Is a Robust Computational Measure of Substituent Steric Effects.

We define ΔGGA as the free energy change for the formal equilibrium: [13]G-H + 1-X-adamantane → [13]G-X + adamantane, where [13]G-H is the C13H22 fragment of all-trans graphane with 3-fold symmetry. This compares with a situation where the group X is equatorial to three cyclohexane rings with one where it is axial to three rings. ΔGGA values vary from 2.9 (CN) to 145.7 kJ mol-1 (CCl3), and this wide range means that ΔG can be calculated with confidence. ΔGGA values for Me, Et, i-Pr, and t-Bu form a regular series, 34.9, 63.3, 101.6, and 142.0, and clearly reflect the steric size of the groups. We propose a model where the six axial hydrogens surrounding X on [13]G-X provide a nearly circular constriction on the substituent close to its point of attachment but which does not extend far above this. We compare these results with A values and with calculations on 2- and 7-substituted [1(2,3)4]pentamantanes. We show that electronic effects on ΔGGA values are negligible but that they correlate well with computed cone and solid angles subtended by the substituent.

Aperiodic structures of rod-shaped precipitates in a Mg-Zn-Al alloy

Rod-shaped precipitates with their long axis parallel to [0001]α commonly form in Mg-Zn-Al alloys, providing strengthening effects. These precipitates are metastable and are generally accepted to be the MgZn2 and/or Mg4Zn7 phases. In this paper, the cross-sectional structure of precipitate rods in an aged ZA84 alloy is examined at the atomic scale using high-angle annular dark-field scanning transmission electron microscopy. It is found that these precipitates are neither pure MgZn2 nor Mg4Zn7. The structures of the rod-shaped precipitates do not have long-range translational symmetry nor long-range 5-fold rotational symmetry in the two-dimensional projection plane perpendicular to the rod long axis. However, these structures can be described by the tiling of different shapes, with four such shapes being most frequently observed. The structural details revealed in this work may help rationalize the many complex precipitate structures in Mg-Zn-Al and Mg-Zn alloys.

Polyphenols Epigallocatechin Gallate and Resveratrol, and Polyphenol-Functionalized Nanoparticles Prevent Enterovirus Infection through Clustering and Stabilization of the Viruses.

To efficiently lower virus infectivity and combat virus epidemics or pandemics, it is important to discover broadly acting antivirals. Here, we investigated two naturally occurring polyphenols, Epigallocatechin gallate (EGCG) and Resveratrol (RES), and polyphenol-functionalized nanoparticles for their antiviral efficacy. Concentrations in the low micromolar range permanently inhibited the infectivity of high doses of enteroviruses (107 PFU/mL). Sucrose gradient separation of radiolabeled viruses, dynamic light scattering, transmission electron microscopic imaging and an in-house developed real-time fluorescence assay revealed that polyphenols prevented infection mainly through clustering of the virions into very stable assemblies. Clustering and stabilization were not compromised even in dilute virus solutions or after diluting the polyphenols-clustered virions by 50-fold. In addition, the polyphenols lowered virus binding on cells. In silico docking experiments of these molecules against 2- and 3-fold symmetry axes of the capsid, using an algorithm developed for this study, discovered five binding sites for polyphenols, out of which three were novel binding sites. Our results altogether suggest that polyphenols exert their antiviral effect through binding to multiple sites on the virion surface, leading to aggregation of the virions and preventing RNA release and reducing cell surface binding.

Single indium atoms and few-atom indium clusters anchored onto graphene via silicon heteroatoms

Single atoms and few-atom nanoclusters are of high interest in catalysis and plasmonics, but pathways for their fabrication and stable placement remain scarce. We report here the self-assembly of room-temperature-stable single indium (In) atoms and few-atom In clusters (2-6 atoms) that are anchored to substitutional silicon (Si) impurity atoms in suspended monolayer graphene membranes. Using atomically resolved scanning transmission electron microscopy (STEM), we find that the exact atomic arrangements of the In atoms depend strongly on the original coordination of the Si anchors in the graphene lattice: Single In atoms and In clusters with 3-fold symmetry readily form on 3-fold coordinated Si atoms, whereas 4-fold symmetric clusters are found attached to 4-fold coordinated Si atoms. All structures are produced by our fabrication route without the requirement for electron-beam induced materials modification. In turn, when activated by electron beam irradiation in the STEM, we observe in situ the formation, restructuring and translation dynamics of the Si-anchored In structures: Hexagon-centered 4-fold symmetric In clusters can (reversibly) transform into In chains or In dimers, whereas C-centered 3-fold symmetric In clusters can move along the zig-zag direction of the graphene lattice due to the migration of Si atoms during electron-beam irradiation, or transform to Si-anchored single In atoms. Our results provide a novel framework for the controlled self-assembly and heteroatomic anchoring of single atoms and few-atom clusters on graphene.

Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.