Absence Of Translational Symmetry Research Articles

Localized Surface Magnon Modes in Cubic Ferromagnetic Lattices

A theoretical formalism for calculating the bulk and surface spin modes in Heisenberg semi-infinite lattices is presented on a ferromagnetic cubic network of spins, coupled via nearest and next-nearest neighbors exchange interactions. The magnetic surface can be considered as semi-infinite slabs at the end of the bulk structures. The breakdown of translation symmetry, in the normal direction of the surface, gives rise to localized spin wave modes in its neighborhood. The localized magnon spectrum is derived as elements of a Landauer-type scattering matrix, in the three cubic lattices sc, bcc and fcc. The magnon properties are simulated and determined numerically for each cubic lattice by using the matching technique. The observed fluctuations in the numerical results demonstrate the interference magnon effects between scattered spinwaves and the localized magnon states, generated by the surface region with characteristic Fano resonances. In cubic leads, the localized surface spin states are sensitive to the local magnetic coupling and the incident direction in the surface boundary. In this contribution, the normalized energy of spinwaves arising from the absence of translation symmetry is analyzed for each cubic system as a function of the exchange integral parameters. This addresses the dependence of the surface magnon on the different possibilities of the of the exchange parameters variation from softening to hardening in the neighborhood of the surface region.

Ab initio modeling of helically periodic nanostructures using CRYSTAL17: A general algorithm first applied to nanohelicenes

A general algorithm based on the line symmetry group theory is proposed for ab initio modeling of one-dimensional (1D) helical nanoobjects using computer codes designed for periodic structure calculations. The key point of the algorithm is the interpolation between the properties of a sequence of periodic structures to obtain the properties of 1D helical nanoobjects without translational periodicity. A special selection of periodic structures avoids excessively long periods, thereby providing control over computational costs. The developed approach gives an opportunity to simulate the continuous dependences of mechanical and electronic properties on the torsional strain for any helical 1D nanoobject using high-level quantum chemical methods. The superposition of torsional and axial deformations can be used to generate the two-parameter maps of the desired properties.The proposed algorithm is applied to obtain the structure and properties of selected nanohelicenes, which are the helicenes infinitely continued along the helical (screw) axis direction. The CRYSTAL17 computer code based on atomic basis set has been used for this purpose. The main advantage of this program in comparison with other widely available ab initio simulation codes is the built-in accounting for helical symmetry operations in 1D periodic systems. Performed calculations show that nanohelicenes have several local minima of potential energy, differing in the order of the helical axis. The irrational order of the helical axis found at all energy minima indicates the absence of translational symmetry in these structures. Two-parameter electronic band gap maps and the dependences of Young’s moduli on the torsion angle for the selected nanohelicenes are calculated and discussed.

Origin of p‐Type Conduction in Amorphous CuI: A First‐Principles Investigation

Recently, Jun et al. (Adv. Mater. 2018, 30, 1706573) reported Sn‐doped amorphous phases of CuI (a‐CuI) as a new class of transparent p‐type semiconductors. It is surprising that high mobilities are found despite amorphous structures tend to localize carriers, particularly the directional p orbitals of anions. To reveal the microscopic origin of the new p‐type amorphous semiconductors, density functional theory calculations are performed, and structural and electrical properties of a‐CuI are investigated. Amorphous models from melt‐quench simulations consist of structural motifs that resemble local orders in crystalline polymorphs of CuI. Despite the absence of translational symmetry, states at valence band maximum (VBM) are substantially extended in linear ways due to the hybridization between I‐5p states, explaining the high hole mobilities in the experiment. Sn‐doped a‐CuI is also investigated and it is found that Sn atoms stabilize the amorphous structure without disturbing the hole transport. Furthermore, results on nonstoichiometric models show that Cu‐deficiency increases the hole concentration in a‐CuI and also enhances the delocalization of VBM states, which is consistent with the experimental observation that the hole mobility increases with doping concentrations. Herein, the origin of hole conduction in amorphous CuI is enlightened, which is believed to contribute in the development of high‐performance p‐type amorphous materials.

Surface wave photonic quasicrystal

In developing strategies for manipulating surface electromagnetic waves, it has been recently recognized that a complete forbidden bandgap can exist in a periodic surface-wave photonic crystal, which has subsequently produced various surface-wave photonic devices. However, it is not obvious whether such a concept can be extended to a quasi-periodic surface-wave system that lacks translational symmetry. Here, we experimentally demonstrate that a surface-wave photonic quasicrystal that lacks short-range order can also exhibit a forbidden bandgap for surface electromagnetic waves. The lower cutoff of this forbidden bandgap is mainly determined by the maximum separation between the nearest neighboring pillars. Point defects within this bandgap show distinct properties compared to a periodic photonic crystal in the absence of translational symmetry. A line-defect waveguide, which is crafted out of this surface-wave photonic quasicrystal by shortening a random row of metallic rods, is also demonstrated to guide and bend surface waves around sharp corners along an irregular waveguiding path.

Aperiodic metal-organic frameworks.

Metal–organic frameworks (MOFs) represent one of the most diverse structural classes among solid state materials, yet few of them exhibit aperiodicity, or the existence of long-range order in the absence of translational symmetry. From this apparent conflict, a paradox has emerged: even though aperiodicity frequently arises in materials that contain the same bonding motifs as MOFs, aperiodic structures and MOFs appear to be nearly disjoint classes. In this perspective, we highlight a subset of the known aperiodic coordination polymers, including both incommensurate and quasicrystalline structures. We further comment upon possible reasons for the absence of such structures and propose routes to potentially access aperiodic MOFs.

Emergent localization in dodecagonal bilayer quasicrystals

A new type of long-range ordering in the absence of translational symmetry gives rise to drastic revolution of our common knowledge in condensed matter physics. Quasicrystal, as such unconventional system, became a plethora to test our insights and to find exotic states of matter. In particular, electronic properties in quasicrystal have gotten lots of attention along with their experimental realization and controllability in twisted bilayer systems. In this work, we study how quasicrystalline order in bilayer systems can induce unique localization of electrons without any extrinsic disorders. We focus on dodecagonal quasicrystal that has been demonstrated in twisted bilayer graphene system in recent experiments. In the presence of small gap, we show the localization generically occurs due to non-periodic nature of quasicrystal, which is evidenced by the inverse participation ratio and the energy level statistics. We understand the origin of such localization by approximating the dodecagonal quasicrystals as an impurity scattering problem.

Parity conservation in electron-phonon scattering in zigzag graphene nanoribbon

In contrast with carbon nanotubes, the absence of translational symmetry (or periodical boundary condition) in the restricted direction of zigzag graphene nanoribbon removes the selection rule of subband number conservation. However, zigzag graphene nanoribbons with even dimers do have the inversion symmetry. We, therefore, propose a selection rule of parity conservation for electron-phonon interactions. The electron-phonon scattering matrix in zigzag graphene nanoribbons is developed using the tight-binging model within the deformation potential approximation.

Characterization of Ar ion etching induced damage for GaN

We studied the overall picture of the etching‐induced damage for GaN films. By using Ar ion etching, we characterized the damage for GaN from various perspectives by AES, transmission electron microscopy, X‐ray absorption spectroscopy, and cathode luminescence. From AES results, it was found that N on GaN surface is selectively etched. After air exposure, the near surface layer within the damage layer was oxidized by the existence of the chemically active dangling bonds. The thickness of the damage layer was observed by cross‐sectional transmission electron microscopy as the dimmed layer, which is caused by the absence of translation symmetry, in other words, degradation of the crystallinity introduced by crystal defects and/or transformation into an amorphous phase in nanoscale. Total reflection X‐ray absorption near‐edge structure spectrum indicated the gradual change from GaN to Ga oxide with higher Ar ion acceleration voltage. Moreover, the etching‐induced nonradiative defects were detected by comparing the cathode luminescence intensities. The various phenomena of the damage can be comprehensively evaluated by using these methods, and the overall picture of etching‐induced damage for GaN was revealed. Copyright © 2011 John Wiley & Sons, Ltd.

Transfer matrix analysis of the elastostatics of one-dimensional repetitive structures

Transfer matrices are used widely for the dynamic analysis of engineering structures, increasingly so for static analysis, and are particularly useful in the treatment of repetitive structures for which, in general, the behaviour of a complete structure can be determined through the analysis of a single repeating cell, together with boundary conditions if the structure is not of infinite extent. For elastostatic analyses, non-unity eigenvalues of the transfer matrix of a repeating cell are the rates of decay of self-equilibrated loading, as anticipated by Saint-Venant's principle. Multiple unity eigenvalues pertain to the transmission of load, e.g. tension, or bending moment, and equivalent (homogenized) continuum properties, such as cross-sectional area, second moment of area and Poisson's ratio, can be determined from the associated eigen- and principal vectors. Various disparate results, the majority new, others drawn from diverse sources, are presented. These include calculation of principal vectors using the Moore–Penrose inverse, bi- and symplectic orthogonality and relationship with the reciprocal theorem, restrictions on complex unity eigenvalues, effect of cell left-to-right symmetry on both the stiffness and transfer matrices, eigenvalue veering in the absence of translational symmetry and limitations on possible Jordan canonical forms. It is shown that only a repeating unity eigenvalue can lead to a non-trivial Jordan block form, so degenerate decay modes cannot exist. The present elastostatic analysis complements Langley's (Langley 1996 Proc. R. Soc. A 452 , 1631–1648) transfer matrix analysis of wave motion energetics.

Localized spin modes on the insulating antiferromagnetic stepped surface model

We present a numerical method to calculate the spin fluctuation dynamics on a stepped surface. The model discussed here consists of an extended antiferromagnetic surface step at the surface boundary of an insulating antiferromagnetic substrate. The stepped surface is formed by two straight steps dropped randomly and the spins moments of the steps and the substrate are considered as local with no electronic effects. The full magnetic problem arising from the absence of translational symmetry due to the presence of a magnetic surface and steps is considered and studied. The calculations concern in particular the energies of localized spin-wave modes near the surface steps and employ the matching procedure in the random-phase approximation and mean field approximation. Only the nearest-neighbor exchange interactions are considered between the spins in the model. The analytical formalism presented here is adapted from an earlier work on the vibrational spectra of two isolated steps, a structure that can be considered as a low dimensional system and solved for the three dimensional evanescent crystal spin field in the bulk and the surface domains around the steps. This spin field arises from the breakdown of the magnetic translation symmetry of the system. The results are used to calculate the spin mode energies associated with the steps and surface terraces. We show the presence of localized acoustic and optical spin wave modes propagating along the surface and the steps as well as the interface surface-steps, their fields are also described as evanescent in the plane normal to the surface step layers and depend on the nature of the exchange interaction near the steps.

Surface and step dynamics of a semi-infinite insulating antiferromagnet system

We have carried out a theoretical study of the localized spin-wave modes near the surface step of the insulating Heisenberg antiferromagnet. In this work, we study the full magnetic problem arising from the absence of translational symmetry due to the presence of a magnetic surface and step. The calculation concerns in particular the spin fluctuation dynamics and employs the matching procedure in the random-phase approximation. Only the nearest neighbours exchange interactions are considered between the spins in the model. The analytical formalism presented here determines the bulk and evanescent spin fluctuation fields in the two-dimensional plane normal to the surface and step regions. The results are used to calculate the localized modes of magnons associated with the step and surface terraces. The present model may be generalized to treat the spin fluctuations dynamics of other extended surface imperfections or nanostructures, provided they preserve the translation symmetry of the ordered spins along a direction in the surface boundary. We show the presence of acoustic and optical localized magnon modes propagating along the surface and the step as well as the interface surface-step, their fields is also described as evanescent in the plane normal to the surface step layer and depends on the nature of the bulk-surface and bulk-step coupling exchanges.

VIBRATIONAL PROPERTIES OF TWO ISOLATED STEPS: A THEORETICAL MODEL

We investigate the dynamical properties of two isolated steps on the surface. We present the solution of the full dynamical problem arising from the absence of translation symmetry in two dimensions due to extended surface steps on the surface boundary of an insulating substrate. The calculations concern in particular the dynamics of localized modes of an atomic step on the surface of a cubic lattice. The theoretical approach determines the vibrational field in both steps. The matching method, which constitutes a powerful formalism for determining the vibrational properties of such disordered surfaces, is used. The model presented in this study consists of two monatomic steps as the interface between three coupled semi-infinite and single semi-infinite atomic layers. The dynamical properties of the perfect waveguides are presented and calculated numerically. The breakdown of translational symmetry perpendicular to the step edges gives rise to several Raleigh-like branches localized in the neighborhood of the steps. Typical dispersion curves for these modes along the steps are given with their polarization.

Surface effects in two-band superconductors: Application toMgB2

Metals with many bands at the Fermi level can have different band dependent gaps in the superconducting state. The absence of translational symmetry at an interface can induce interband scattering and modify the superconducting properties. We dicuss the relevance of these effects to recent experiments in MgB$_2$.

NMR and Susceptibility Studies of QuasicrystallineAl-Mn-Si-Ru Alloys

Magnetic susceptibility and nuclear magnetic resonance measurements have been made on quasicrystalline and crystalline phases of Al 62 Mn 20 Si 10 Ru 8 and Al 68 Mn 20 Si 6 Ru 6 alloys. The average value of local magnetic moment on Mn atoms and the spin-glass freezing temperature are not different so much between the two phases. However, static and dynamical properties of 27 Al NMR signals observed in the two phases are significantly different. These results suggest that most of the magnetic properties such as the formation of local magnetic moments and the magnitude of interactions between them are not closely related with the presence or absence of translational symmetry of the lattice; these properties might be related with local atomic configuration. A characteristic property of electrons in the present quasicrystals has been demonstrated by the transferred hyperfine interactions between Mn atoms and Al nuclei.

Interatomic forces near a defect: The impurity-susceptibility method

A strongly perturbing defect in a metal, like a H + particle, is not only a force centre repelling or attracting its neighbours but it modifies considerably the interatomic forces between them. The relevant quantity determining the nature of these forces is, in metals, the dielectric susceptibility of the inhomogeneous impurity-in-jellium system. The absence of translational symmetry in the polarizability leads to a ‘bipolar’ screening and, thereby, to non-central interactions between the neighbouring atoms. Exact asymptotic formulae have been found for the independent-particle polarizability including bound and scattered states, assuming predominantly s-scattering at the impurity. A semi-quantitative study of the atomic interactions in the ‘impurity-in-jellium’ background is given for a simplified theoretical model which allows for an analytic approach and is, nevertheless, expected to reproduce the main features of forces in a dilute hydride system.

Substrate influences on explosively crystallized amorphous germanium films

The structure of amorphous Ge can be most satisfactorily described by a continuous random network model. The basic features of this random network for amorphous Ge are the total absence of translational symmetry combined with tetrahedrally coordinated atoms whose bond angles are as close to the ideal tetrahedral angle of 109° 28’ as possible. Non-crystallinity is achieved through variations in the tetrahedral angle and through relative rotations of adjoining tetrahedra. The local structure is thus well-defined. The medium range structure is, however, subject to debate as a number of physical properties, such as optical absorption and electrical conductivity, have been found to be highly sensitive to deposition conditions and heattreatment. The purpose of the present work was to use the phenomenon of explosive crystallization as a probe to investigate the medium range structure of amorphous Ge. Inhomogeneities in the medium range structure were expected to influence the morphology of the explosively crystallized foils.