Phonon-polariton density of states in semiconductor superlattices

An interesting property of modulated semiconductor materials is that their reflectance and absorption spectra can nearly be chosen at will by adjusting the layer geometry. Introducing the concept of phonon-polariton density of states, this paper is aimed at investigating spectral properties of multilayered materials in the infra-red frequency range. Using powerful analytical methods, we will successively consider the cases of infinite and semi-infinite superlattices. The local density of states of polariton modes is obtained using a Green's function technique. Complete information is then available on allowed radiative and non-radiative electromagnetic excitations, (as a function of frequency and wavelength), at any depth in the stratified material. This approach will depict the essential role played by the surface, which changes significantly the polariton density of states as compared to ideal unbounded materials. In multilayered materials, in addition to the effect induced by the surface, one can similarly investigate the influence of the internal interfaces on the polariton local density of states and, from these, on the optical properties of those systems. Electromagnetic eigenmodes arising from the accumulation of interfaces are crucial to assess the spectral properties involving TM-polarized radiations. Effects related to the TE-polarized radiations are explained from the macroscopic anisotropy due to the alternate growth of different semiconductors. These results will be used to discuss reflectance experiments and simulated ATR spectra.     

Strong-coupling expansions for multiparticle excitations: continuum and bound states

We present a new linked cluster expansion for calculating properties of multiparticle excitation spectra to high orders. We use it to obtain the two-particle spectra for systems of coupled spin-half dimers. We find that even for weakly coupled dimers the spectrum is very rich, consisting of many bound states. The number of bound states depends on both geometry of coupling and frustration. Many of the bound states can only be seen by going to sufficiently high orders in the perturbation theory, showing the extended character of the pair attraction.     

An efficient technique for the multilayered microwave and millimeter planar waveguides

The method of lines is extended to the multilayered inhomogenous dielectric layers by means of the additional transformation and the recurrence matrix. The computed dispersion diagrams for the multilayered planar waveguides agree very well with the results from other authors. New results for a six layer structure are given.     

Correct application of Fresnel’s equations for intensity analysis of angle-resolved photoemission data

The electromagnetic field relevant for the excitation process in angle-resolved photoemission is studied. We show that Fresnel’s equations together with the known bulk dielectric constants can be used to calculate the complex vector potential at the metal surface. A model is developed which accounts correctly for the special experimental geometry with focused light. It is used to calculate the variation of photoemission intensity with changing light incidence angle and polarization. Experimental data for the photoemission intensity as a function of light incidence angle are presented for direct transitions out of bulk, surface and adsorbate states at a Cu(1 1 0) surface. The comparison to our model shows that the application of copper bulk optical constants is justified even when electronic states are localized to the topmost atomic layer.     

Triangle Geometry for Qutrit States in the Probability Representation

We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the statistics of classical systems with three random vector variables and three classical probability distributions obeying special constrains found in this study. The Bloch spheres geometry of qubit states is mapped onto triangle geometry of qubits. We investigate the triada of Malevich’s squares describing the qubit states in quantum suprematism picture and the inequalities for the areas of the squares for qutrit (spin-1 system). We expressed quantum channels for qutrit states in terms of a linear transform of the probabilities determining the qutrit-state density matrix.     

Work functions and surface double layer potentials of monovalent metals from a network model

The model described in this paper uses an electronic wave function which is defined to be nonzero only along the lines connecting first nearest neighbors in the metallic lattice. The electrons are assumed to move freely along the lines between nearest neighbors. No electron-electron or electron-nucleus force is included in the model calculations (except for forces arising from the Pauli exclusion principle). The work function is defined as the amount of energy required to move an electron from a point slightly inside the crystal to a point slightly outside. The contribution of the electronic double layer is included in the calculation of the work function as well as the dependence of the double layer potential on the surface geometry. Surface states, where the electron is localized in the neighborhood of the face of the crystal, are found to have energies sufficiently above the Fermi level to eliminate the possibility that they make any contribution to the double layer potential for the case of the (100) crystal plane. Consequently, surface states have been ignored in all the calculations. The surface double layer is assumed to be caused by the presence of a finite potential barrier at the surface of the crystal. Bulk electronic wave functions can penetrate this barrier and decay exponentially outside the crystal. The only parameters required by the model are the nearest neighbor distance for the lattice and the height of the potential barrier at the surface. The former quantity is fixed by the lattice structure (body centered cubic for the alkali metals) and by the density, while the latter quantity can be adjusted to give the best agreement between the model calculations and experiment. For the alkali metals, lithium through sodium, the best value of the barrier height is about 50% of the sum of the ionization potential energy, the heat of vaporization, and the calculated Fermi level for the corresponding metal. In addition, the value of the double layer potential for sodium agrees very well with a more sophisticated calculation by Bardeen and is reasonably close to the experimental measurement.     

柱面分层流体饱和孔隙地层中的声波测井波场模拟

因钻井作业时泥浆侵入等因素,井外介质沿径向常呈现非均匀性。本文将地层视为柱面分层孔隙介质,采用传递矩阵法模拟声波测井波场。注意到慢纵波波数的实部和虚部都很大,当井外含大厚度层且频率较高时,易因计算大自变量的Hankel函数而溢出,我们在波场表达式中引入了归一化的Hankel函数。论文将前人模拟关于柱面分层固体弹性介质声波测井的广义反射/透射系数计算方法推广到了分层孔隙介质情况,导出了波幅系数的计算公式,并针对含侵入带的柱面分层孔隙地层,计算了声波测井全波波形。      

Charged excitons in quantum dots: novel magnetic behavior and Auger processes

We describe theoretically multiply-charged excitons interacting with a continuum of delocalized states. Such excitons exist in relatively shallow quantum dots and have been observed in recent optical experiments on InAs self-assembled dots. The interaction of an exciton and delocalized states occurs via Auger-like processes. To describe the optical spectra, we employ the Anderson-like Hamiltonian by including the interaction between the localized exciton and delocalized states of the wetting layer. In the absence of a magnetic field, the photoluminescence line shapes exhibit interference effects. When a magnetic field is applied, the photoluminescence spectrum demonstrates anticrossings with the Landau levels of the extended states. We show that the magnetic-field behavior of charged excitons is very different to that of diamagnetic excitons in three and two-dimensional systems.     

PbTe(001)表面原子几何结构和电子结构的第一性原理计算

用第一性原理的密度泛函理论计算了PbTe（001）表面的几何结构和电子结构.计算结果表明：PbTe（001）表面不发生重构，但表面几层原子表现出明显的振荡弛豫现象，其中第一、第二层间距减小4.5%，第二、第三层间距增加2.0%，并且表面层原子出现褶皱.表面带隙在X 点，带隙变宽，在基本带隙中不引入新的表面态，而导带底和价带顶附近等多处出现新的表 面共振态；弛豫后费米面处态密度很低，所以表面结构很稳定. 关键词： 密度泛函理论 表面几何结构 表面电子结构 PbTe     

新型波导多层光存储信息读出光学系统设计

信息读出光学系统是波导多层存储方法的重要组成部分,从几何光学角度,提出了两种信息读出光学系统的理论设计,并对两种系统的特点进行了实验研究,结果表明两种光学系统都是可行的,而且对波导多层光存储的进一步研究及实用化都有一定的参考价值。     

Anisotropic intermolecular forces. I. Rare gas—hydrogen chloride systems

Anisotropic potential energy surfaces for Ne.HCl, Kr.HCl and Xe.HCl are obtained by simultaneous least squares fitting to molecular beam spectra and rotational line broadening cross sections. A revised potential surface for Ar.HCl is also presented. The potentials are all very similar in shape, with the absolute minimum at the linear rare gas-HCl geometry in each case. The absolute well depths and well depth anisotropies increase steadily as the size of the rare gas atom increases.

The potentials should be reliable in the region of the absolute minimum and on the repulsive wall of the potential. The molecular beam spectra for Ne.HCl can be fitted only by a potential with a significant secondary minimum at the linear Ne.Cl-H geometry, but the existing data for the more anisotropic Ar, Kr and Xe systems are not sensitive to the presence of this potential feature. The potential surfaces for these systems have accordingly been constrained to have a similar secondary minimum near the linear rare gas-ClH geometry. Experiments which would provide further information on the intermolecular potentials are suggested and predictions of the results are made.     

Analytic expression of the temperature increment in a spin transfer torque nanopillar structure

The temperature increment due to the Joule heating in a nanopillar spin transfer torque system is investigated. We obtain a time-dependent analytic solution of the heat conduction equation in nanopillar geometry by using the Green's function method after some simplifications of the problem. While Holm's equation is applicable only to steady states in metallic systems, our solution describes the time dependence and is also applicable to a nanopillar-shaped magnetic tunneling junction with an insulator barrier layer. The validity of the analytic solution is confirmed by numerical finite element method simulations and by the comparison with Holm's equation.     

Quantum mechanics on manifolds embedded in Euclidean space

Quantum particles confined to surfaces in higher-dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when confinement is implemented by forces that act normal to the surface. We review this confining potential formalism applied to the confinement of a particle to an arbitrary manifold embedded in a higher-dimensional Euclidean space. We devote special attention to the geometrically induced gauge potential that appears in the effective Hamiltonian for motion on the surface. We emphasize that the gauge potential is only present when the space of states describing the degrees of freedom normal to the surface is degenerate. We also distinguish between the effects of the intrinsic and extrinsic geometry on the effective Hamiltonian and provide simple expressions for the induced-scalar potential. We discuss examples including the case of a three-dimensional manifold embedded in a five-dimensional Euclidean space.     

Multiple optical interactions for quantum gates

We present results of quasi-phase matching (QPM) interactions in one-dimensional multilayered media consisting of layers with different χ⁽²⁾ nonlinearities that interchanged by linear dispersive layers. We exploit the idea of manipulating overall group delay mismatches between the various fields in each layer by appropriate choosing of the dispersive parameters and consider both multiple optical QPM interactions and preparation of pure photon states in application to quantum gates.     

General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye--Hückel Regime

We study the statistical mechanics of classical Coulomb systems in a low coupling regime (Debye--Hückel regime) in a confined geometry with Dirichlet boundary conditions for the electric potential. We use a method recently developed by the authors which relates the grand partition function of a Coulomb system in a confined geometry with a certain regularization of the determinant of the Laplacian on that geometry with Dirichlet boundary conditions. We study several examples of fully confining geometry in two and three dimensions and semi-confined geometries where the system is confined only in one or two directions of the space. We also generalize the method to study systems confined in arbitrary geometries with smooth boundary. We find a relation between the expansion for small argument of the heat kernel of the Laplacian and the large-size expansion of the grand potential of the Coulomb system. This allow us to find the finite-size expansion of the grand potential of the system in general. We recover known results for the bulk grand potential (in two and three dimensions) and the surface tension (for two-dimensional systems). We find the surface tension for three-dimensional systems. For two-dimensional systems our general calculation of the finite-size expansion gives a proof of the existence a universal logarithmic finite-size correction predicted some time ago, at least in the low coupling regime. For three-dimensional systems we obtain a prediction for the curvature correction to the grand potential of a confined system.     

Effect of graded interlayer on the mode I edge delamination by residual stresses in multilayer coating-based systems

The mode I edge delamination could be initiated due to the presence of the interfacial peeling stresses near the edges of the multilayered systems due to the material mismatches between the adjacent layers. However, the exact peeling stress distributions could not be obtained by using the existing analytical and numerical models. It was proposed recently that the peeling moment resulting from the localized peeling stresses could be used to characterize mode I edge delamination. In this paper, the effect of the graded interlayer on the mode I edge delamination by thermal residual stresses in multilayer coating-based systems was investigated. Following the previous analysis approaches, the exact closed-form solutions for the peeling moments at individual interfaces and the curvatures for bilayer system, typical thermal barrier coating (TBC) system and TBC-based system with a graded interlayer inserted between the metallic layer and the ceramic layer were, respectively, derived. Case studies showed that the edge delamination by thermal stress could be impeded by properly selecting the coating materials and individual layer thicknesses. These studies may provide some important insights for developing fail-safe designing methodologies for multilayered systems.     

Coulomb self-energy and electrostatic potential of a uniformly charged square in two dimensions

The most popular model for a two-dimensional electronic system considers electrons moving in a background of uniform positive charge. Studies of finite systems employing a spherical geometry (electrons on the surface of a sphere) or a disk geometry background are numerous. The same cannot be said for a square geometry, who after all, would be the geometry of choice for quantum Hall states in a Landau gauge. A background represented by a uniformly charged square seems to be perceived as too costly from a computational point of view. By using simple transformations, we show that the Coulomb self-energy and the electrostatic potential of a uniformly charged square can be exactly calculated and poses no difficulty. The current results can be used in systematic studies of properties of finite systems of electrons embedded in a positive background in the form of a uniformly charged square.     

Geometry optimization of a barrel silicon pixelated tracker

We have studied optimization of the design of a barrel-shaped pixelated tracker for given spatial boundaries. The optimization includes choice of number of layers and layer spacing. Focusing on tracking performance only,momentum resolution is chosen as the figure of merit. The layer spacing is studied based on Gluckstern's method and a numerical geometry scan of all possible tracker layouts. A formula to give the optimal geometry for curvature measurement is derived in the case of negligible multiple scattering to deal with trajectories of very high momentum particles. The result is validated by a numerical scan method, which could also be implemented with any track fitting algorithm involving material effects, to search for the optimal layer spacing and to determine the total number of layers for the momentum range of interest under the same magnetic field. The geometry optimization of an inner silicon pixel tracker proposed for BESIII is also studied by using a numerical scan and these results are compared with Geant4-based simulations.     

Thermodynamics on noncommutative geometry in coherent state formalism

The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual “attraction (repulsion) potential” between boson (fermion) in the high temperature limit. The characters could be traced to the fact that, the particle with mass m in noncommutative thermal geometry with noncommutativity θ and temperature T will correspond to that in the commutative background with temperature T(1+kTmθ)⁻¹. Such a correspondence implies that the ideal gas energy will asymptotically approach to a finite limiting value as that on commutative geometry at T_θ=(kmθ)⁻¹. We also investigate the squeezed coherent states and see that they could have arbitrary mean energy. The thermal properties of those systems are calculated and compared to each other. We find that the heat capacity of the squeezed coherent states of boson and fermion on the noncommutative geometry have different values, contrast to that on the commutative geometry.