Surface Green Function Research Articles

Surface-Induced Magnetic Anisotropy of Impurities

We present theoretical and numerical studies of the magnetic anisotropy energy of an atomic-like impurity near the surface of a metallic host (Au). The valence band of the host metal is described in terms of a realistic tight-binding surface Green's function technique. We compare two models: (i) when spin-orbit coupling is taken into account in the d-band of the host and (ii) when the impurity's d-level experiences strong spin-orbit splitting. The level splitting of the impurity's spin-states is calculated in leading (first or second) order of the exchange interaction between the impurity and the host atoms. It is shown that the magnetic anisotropy constant is an oscillating function of the distance d of the impurity from the surface. For large distances, an asymptotic analysis implies that the period of these oscillations is determined by the extremal vectors of the host's Fermi Surface and the amplitude decays as 1/d2. Our numerical results clearly suggest that the host-induced magnetic anisotropy energy is by several orders smaller in magnitude than the one originating from a strong local spin-orbit coupling.

Surface Green Function With Surface Stresses and Surface Elasticity Using Stroh’s Formalism

Abstract In the present paper, surface Green functions in an anisotropic elastic half-domain subjected to a concentrated force and a line force are derived using Stroh’s formalism considering surface stress and surface elasticity. Formulation of the boundary condition based on Stroh’s formalism is presented and is used to derive the surface Green functions. The displacement field far from the surface is affected only slightly by the surface stress and elasticity. However, the stress field is influenced to a somewhat greater degree by the surface stress and elasticity. The influence of the mechanical properties of the surface on the distributions of displacement and stress near the surface is investigated for various values of surface elastic modulus and surface stress. The surface stress and surface elasticity affect the displacements and stresses, respectively, in different manners. Displacement fields in molecular dynamics are compared with those in the Green function, and it is shown that the results are in fair agreement.

Elastic interaction between force dipoles on a stretchable substrate

The objective of this paper is to study elastic interaction between force dipoles on the surface of a semi-infinite stretchable substrate. The substrate undergoes a uniform, finite pre-stretch, while the additional deformation induced by a force dipole is assumed infinitesimal. By adopting a neo-Hookean constitutive law, the surface Green function for the pre-stretched substrate is obtained. The result is then used to derive the energy of dipolar interaction on the surface. As an application, mutual interaction between two physisorbed molecules is discussed in detail. The dipole moment of a molecule is found from the elementary intermolecular potential, and its dependence on the pre-stretch is established explicitly. Numerical results indicate that pre-stretches can substantially alter the interaction, and thus provide a controllable way to guide the self-assembly of adsorbed molecules on the substrate surface.

Interference effect in scattering loss of high-index-contrast planar waveguides caused by boundary reflections

We present theoretical and experimental results on an interference effect caused by boundary reflections on the optical scattering loss in high-index-contrast planar waveguides. Analytical expressions for the polarization-dependent scattering loss are derived using a surface Green's function. For high-index-contrast waveguides of submicrometer dimensions a significant deviation from accepted theory arises, including scattering loss suppression owing to a thin-film interference effect. Our theoretical predictions are confirmed by loss measurements on silicon-on-insulator channel waveguides.

Magnetic barriers in graphene nanoribbons: Theoretical study of transport properties

A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of the conductance steps toward higher energies. The magnetic barrier also induces Fabry--P\'erot-type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevents confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbons tend to localize the lowest propagating state, which get delocalized in the magnetic barrier region. Thus, in sharp contrast to the case of two-dimensional graphene, the charge carriers in graphene nanoribbons cannot be confined by magnetic barriers. We also present a method based on the Green's function technique for the calculation of the magnetosubband structure, Bloch states and magnetoconductance of the graphene nanoribbons in a perpendicular magnetic field. Utilization of this method greatly facilitates the conductance calculations, because, in contrast to existing methods, the present method does not require self-consistent calculations for the surface Green's function.

Treatment of the asymptotic behaviour of the piezolectric Green's function for finite element/boundary element analysis of surface waveguides

The simulation of surface waveguides has been dramatically improved by the combination of analytic description of piezoelectric materials using surface Green's function and numerical approaches sur as plane wave expansion, finite diffrence, finite element, etc. A lot of work has been dedicated to treat the singularities of such Green's function generally derived in the spectral domain. An interesting approach consists in using the Green's function which relates the surface stresses to the displacements which is particularly well‐suited for mixed finite element/boundary element formulations. This Green's function does not exhibit any pole but presents an asymptotic behavior which tends to infinity along increasing wavenumber values, which prevents the computation of its Fourier transform. In this work, we show how this difficulty can be overcome and we propose a formulation in which the Green's function is factorized in order to change its asymptotic behaviour to a form allowing for Fourier transform computation for non periodic problems and an analytic treatment of its asymptotic behaviour for the simulation of periodic structures. Examples are provided to show the interest of the proposed approach in terms of computation delays and precision.

Quantum thermal transport in nanostructures

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures.

Atomistic non-equilibrium Green’s function simulations of Graphene nano-ribbons in the quantum hall regime

The quantum Hall effect in Graphene nano-ribbons (GNR) is investigated with the non-equilibrium Green’s function (NEGF) based quantum transport model in the ballistic regime. The nearest neighbor tight-binding model based on p z orbital constructs the device Hamiltonian. GNRs of different edge geometries (Zigzag and Armchair) are considered. The magnetic field is included in both the channels and contact through Peierls substitution. Efficient algorithms for calculating the surface Green function are used to reduce computation time to enable simulating realistically large dimensions comparable to those used in experiments. Hall resistance calculations exactly reproduce the quantum Hall plateaus observed in the experiments. Use of large dimensions in the simulation is crucial in order to capture the quantum Hall effect within experimentally magnetic fields relevant 10–20 T.

1211 表面応力と表面弾性定数を考慮した弾性理論による表面近傍の変形解析(S05-3 ナノ・マイクロ材料の強度・信頼性(3)ナノ・マイクロ材料の強度物性評価,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

We derived three-dimentional surface Green function in anisotropic materials for a concentrated force considering surface stress and surface elasticity. Surface Green function can be expressed the displacement field adhering an atom. In this paper, displacement fields near surface in Fe adhering some atoms are calculated using Green function and molecular dynamics, and those are compared with each other.

SPM NUMERICAL RESULTS FROM AN EFFECTIVE SURFACE IMPEDANCE FOR A ONE-DIMENSIONAL PERFECTLY-CONDUCTING ROUGH SEA SURFACE

From the analytical theory of rough surface Green's function based on the extension of the diagram method of Bass, Fuks and Ito, with the smoothing approximation, numerical results are presented for Gaussian and sea spectra and compared with a benchmark method by considering a one-dimensional perfectly conducting Gaussian rough surface. The effects of multiple scattering due to the surface roughness are incorporated systematically into the solutions through an effective surface impedance, which can be iterated up to the second-order. In addition, comparisons of the bistatic scattering coefficients are presented with the first- and second- orders conventional small perturbation method. This study will be useful for remote sensing of the ocean surface, especially when the transmitter is close to the surface.

THE ELECTROSTATIC POTENTIAL ASSOCIATED TO INTERFACE PHONON MODES IN NITRIDE SINGLE HETEROSTRUCTURES

The electrostatic potential associated to the interface oscillation modes in nitride- based heterostructure is calculated with the use of a complete phenomenological electroelastic continuum approach for the long wave optical oscillations, and the Surface Green Function Match- ing technique. The crystalline symmetries of zincblende and -isotropically averaged- wurtzite are both considered in the sets of input bulk frequencies and dielectric constants.

First-principles calculation of charge transfer at surfaces: The case of core-excitedAr*(2p3∕2−14s)on Ru(0001)

We present an ab initio scheme for the calculation of the resonant charge transfer of electrons at surfaces. The electron initially resides in a bound resonance, i.e., appearing below the vacuum level, associated with a core-excited adsorbate. Our treatment is based on first-principles density-functional calculations of this initial situation using finite slabs. These results are combined with bulk calculations of the substrate material to obtain the Hamiltonian of the semi-infinite system in which the electron evolves. Therefore, we include a realistic description of the electronic structure of both subsystems, substrate and adsorbate, and the interaction between them. The surface Green's function is then computed using the transfer matrix method and projected onto a wave packet localized in the adsorbate. The width and energy of the resonance can be obtained from an analysis of the projected Green's function, and the charge transfer time can be estimated. The calculated width is independent of the wave packet used for the projection, at least as far as there are not several overlapping resonances at neighboring energies. Alternatively, one can directly calculate the time evolution of the population of the initial wave packet. Both alternatives are presented and compared. Our first-principles calculations are based on periodic arrangements of adsorbates on the surface. With an appropriate average of the ${\mathbf{k}}_{\ensuremath{\parallel}}$ resolved results, one can extrapolate to the limit of an isolated adsorbate. We discuss several possibilities to do this. As an application, we focus on the case of the $4s$ bound resonance of a core-excited ${\mathrm{Ar}}^{*}(2{p}_{3∕2}^{\ensuremath{-}1}4s)$ adsorbate on Ru(0001), for which there are extensive experimental studies. The calculated values and trends are in good agreement with the experimental observations.

Simulation of phonon transport across a non-polar nanowire junction using an atomistic Green’s function method

Phonon transport across a non-polar nanowire situated between two semi-infinite contacts is simulated in this paper using the atomistic Green's function method. Abrupt geometric changes between the nanowire and bulk contacts are handled by self-energy matrices obtained from bare surface Green's functions. Transport properties such as phonon transmission functions and thermal conductances are calculated, and their dependencies on the interatomic potential, length, diameter, shape, and lattice orientation are investigated. The results reveal that the overall thermal conductance of the nanowire\char21{}bulk-contact structure increases with nanowire diameter while the normalized thermal conductance approaches an asymptotic value. Thermal conductance decreases significantly with increasing nanowire length and converges to that of the single-contact case. This method can be generalized to study phonon transport through a variety of nanostructures between bulk contacts.

Quasi-bound electronic states in parabolic GaAs/AlGaAs quantum wells and barriers

A full quantum-mechanical description of the quasi-bound states in parabolic quantum wells and barriers is presented. The GaAs/AlGaAs heterostructures are considered within the framework of the semi-empirical sp3s* spin dependent tight-binding model and the surface Green function matching method (SGFM). Series of equidistant energy quasi-bound states are observed in the continuous spectrum and their FWHM and mean life time are calculated. Strong energy and spatial localizations are found in correlation with the large mean life times.

Study of the electronic fundamental transition of zincblende InN/InGaN quantum wells

In this work we calculate the transition energy from the first level of holes to the first level of electrons (1h–1e) for cubic InN/InxGa1-xN quantum wells. We employ the empirical tight binding approach with a sp3s* orbital basis, nearest neighbors interactions and the spin–orbit coupling, together with the surface Green function matching method. Our tight binding parameters give a value of 0.65eV for the InN gap and 3.3eV for GaN. For the InxGa1-xN alloy we use the virtual crystal approximation. We study the transition energy behavior varying the well width for concentrations x=0.2, 0.5, and 0.8. For the calculations, we use two values of the valence band offset: 30% and 50%. We take into account the strain in the well, due to the different lattice constants between the well and the barrier.

Ab Initio Calculation of a Graphene-Ribbon-Based Molecular Switch

We perform ab initio calculations of electronic and transport properties of nanoelectronic systems. The surface Green's function of semi-infinite ribbons made from graphene sheets is constructed fr...

The Simulation of Ship Motions Using a B-Spline–Based Panel Method in Time Domain

In this paper, a B-spline-based higher-order method is developed for simulating three-dimensional ship motions with forward speed. The problem is formulated in time domain using a transient free surface Green function. The body geometry is defined by open uniform or nonuniform B-spline basis functions depending on the hull type, whereas the unknown field variables are described by open uniform B-spline basis functions. The collocation method is applied to discretize the integral equation and then solved for the unknown potentials and source strengths. Motion computations in head waves are carried out for three types of ship hulls: a mathematically defined Wigley hull, a typical containership (S175 hull), and a Series 60 hull. Results are obtained for regular and irregular waves and compared with available experimental and computational results. It is found that the results from the present method are in very good agreement with the published results, and in particular with experimental data. Long-duration simulations have also been carried out with an ordinary desktop PC (PIV with 512 MB RAM) to demonstrate the ability of the method to simulate motions over long periods without any visible deterioration using only modest computational resources.

Surface Green functions in molecular transport junctions: Generalization to interacting electrons in the leads

Surface Green functions in molecular transport junctions: Generalization to interacting electrons in the leads

Surface segregation energy in bcc Fe-rich Fe-Cr alloys

The exact muffin-tin orbitals (EMTO) technique in conjunction with the coherent-potential approximation (CPA) as well as the projector-augmented-wave (PAW) method have been used to calculate the surface segregation energy of Cr at the (100) surface of Fe-rich bcc Fe-Cr alloys. We find that PAW results strongly depend on the supercell size used in the calculations. In particular, for large supercells, the surface segregation energy of Cr is positive, which means that Cr should not segregate toward the surface of diluted alloys. This is in agreement with our EMTO-CPA results as well as previous surface Green's-function calculations. However, the surface segregation energy of Cr is negative if small unit cells are used for simulations. This is in agreement with previous full-potential supercell calculations. We explain such a size dependence by a peculiar concentration dependence of interatomic interactions in ferromagnetic Fe-Cr alloys.

Surface Green’s function calculations: A nonrecursive scheme with an infinite number of principal layers

A novel computational method for a surface Green's function matrix is introduced for the calculation of electrical current in molecular wires. The proposed nonrecursive approach includes an infinite number of principal layers and yields the second-order matrix equation for the transformed Green's function matrix. The solution is found by the direct diagonalization of the auxiliary matrix without any iteration process. As soon as complex roots of the auxiliary matrix (approximately GS) are calculated, the gaps and the bands in the surface electronic structure are found. It is shown that the solution of a second-order matrix equation determines the spectral density matrix, that is, the density of states for noninteracting electrons. Single and double principal layer models are studied both analytically and numerically. The energy interval for nonvanishing spectral matrices is determined. This method is applicable to matrices of any rank.