Spectral Analysis of Unitary Band Matrices

 This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems. These doubly infinite matrices essentially depend on an infinite sequence of phases which govern their spectral properties. We prove the spectrum is purely singular for random phases and purely absolutely continuous in case they provide the doubly infinite matrix with a periodic structure in the diagonal direction. We also study some properties of the singular spectrum of such matrices considered as infinite in one direction only. Received: 29 April 2002 / Accepted: 7 August 2002 Published online: 20 January 2003 Communicated by B. Simon     

铁磁非铁磁夹层中电子自旋波的传输及应用

建立了有限对一维铁磁性和非磁性层交错组成的周期系统, 应用布洛赫自旋波量子理论, 研究了该系统的基本性质及电子波函数散射特征对交错层数量依赖的关系. 研究发现: 在系统中电子波函数可表示为无限周期系统中转换矩阵特征向量的叠加或类布洛赫函数, 解此函数可得到任意层数系统的单色波散射的精确解. 在此基础上, 导出了电子波函数在周期系统中反射系数和透射系数对能量的依赖关系. 对光谱窗口的计算发现其势能和宽度几乎与全反射区域一样. 该系统由于高能量的传输和在电子自旋方向上对交换能的依赖而可能用于自旋滤波器. 关键词： 磁性多层膜 铁磁性和非磁性结构 电子散射 电子自旋滤波器     

Scattering theory of electron transport in single layer graphene with a time-periodic potential

We applied the scattering approach to studying the transport properties of charge carriers through single layer graphene in the presence of a time-periodic potential. Using the method, expressions for the second-quantized current operator, conductivity and shot noise are obtained. The results obtained in this study demonstrate that the applied external field provides sidebands for charge carriers to tunnel through the graphene, and these sidebands changed the transport properties of the system. The results obtained in this study might be of interest to basic understanding of photon-assisted tunneling (PAT) and designers of electron devices based on graphene.     

Ballistic electron propagation through periodic few-layer graphene nanostructures

We have studied electron propagation in periodic structures containing mono- and few-layer graphene regions and/or semiconducting stripes. The calculation of the transmission coefficient in all cases has been performed using transfer matrices inside regions with the same material/potential energy, as well as interface matrices between regions in which the evolution laws of charge carriers differ. Numerical simulations of the transmission coefficient, as well as of the low-temperature conductance, suggest that different periodic structures modulate differently the electrical current. The obtained results can be used to model ballistic transport in all-graphene devices, in particular in few-layer graphene structures.     

Real‐Time and Broadband Terahertz Wave Scattering Manipulation via Polarization‐Insensitive Conformal Graphene‐Based Coding Metasurfaces

Here, for the first time, the real‐time and broadband manipulation of terahertz (THz) waves are acquired by introducing a multifunctional graphene‐based coding metasurface (GBCM). The designed structure consists of subwavelength patterned graphene units whose operational statuses can be dynamically switched between two digital states of “0” and “1”. By engineering the spatial distribution of chemical potentials across the GBCM, various scattering patterns having single, two, four, and numerous reflection beams are elaborately achieved just within one planar structure. To compute the far‐field pattern of GBCM, an inverse discrete Fourier transform (IDFT) is established, providing a fast and efficient design method. The proposed GBCM provides a low reflection bellow ?10 dB over a broad frequency band ranging from 1 THz to 1.9 THz. In addition, the metasurface retains its low reflection behavior in a wide range of incident wave angles for both TE and TM polarizations. According to conformal invariance of graphene sheets, the stealth property of GBCM is well preserved while wrapping around a curved object. The proposed technique of real‐time scattering manipulation leads to multifunctional THz devices, opening new routes contributing to numerous applications such as imaging and stealth technology.     

Analytical Solution of Partial-Wave Faddeev Equations with Application to Scattering and Statistical Mechanical Properties

In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent.The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles(bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length,phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.     

Analytical Solution of Partial-Wave Faddeev Equations with Application to Scattering and Statistical Mechanical Properties

In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent. The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles (bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length, phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.     

All‐Optical Photonic Band Control in a Quantum Metamaterial

Metamaterials made of periodic collections of dielectric nanorods are considered theoretically. When quantum resonators are embedded within the nanorods, one obtains a quantum metamaterial, whose electromagnetic properties depend upon the state of the quantum resonators. The theoretical model predicts that when the resonators are pumped and reach the inversion regime, the quantum metamaterial exhibits an all‐optical switchable conduction band. The phenomenon can be described by considering the pole stucture of the scattering matrix of the metamaterial.     

A general method for analyzing em wave scattering from arbitrarily shaped two-dimensional periodic surfaces

In this paper the Method of Lines (MoL) is successfully extended to solve the EM wave scattering problems of periodic surfaces with arbitrary profile. As examples, the scattering coefficients of space harmonics of corrugated and sinusoidal surfaces are calculated. The results are in good agreement with available data from Wirgin and from A.K.Jordan et al. In addition, the results of comb structure are also calculated. The flexibility and less computation of this method make it eligible for analyzing various two-dimensional periodic structures.     

Quantum Transport in the Black‐Hole Configuration of an Atom Condensate Outcoupled Through an Optical Lattice

The outcoupling of a Bose‐Einstein condensate through an optical lattice provides an interesting scenario to study quantum transport phenomena or the analog Hawking effect as the system can reach a quasi‐stationary black‐hole configuration. We devote this work to characterize the quantum transport properties of quasi‐particles on top of this black‐hole configuration by computing the corresponding scattering matrix. We find that most of the features can be understood in terms of the usual Schrödinger scattering. In particular, a transmission band appears in the spectrum, with the normal‐normal transmission dominating over the anomalous‐normal one. We show that this picture still holds in a realistic experimental situation where the actual Gaussian envelope of the optical lattice is considered. A peaked resonant structure is displayed near the upper end of the transmission band, which suggests that the proposed setup is a good candidate to provide a clear signal of spontaneous Hawking radiation.     

Linear differential equations for the one‐dimensional scattering problem

The transmission and reflection amplitudes of an electron moving in a one dimensional potential of arbitrary form are obtained using the transfer matrix method. It is shown that the one‐dimensional scattering problem, in its most general form, can be reduced to Cauchy problem for a set of two linear differential equations.     

单空位缺陷对石墨纳米带电子结构和输运性质的影响

基于第一性原理电子结构和输运性质计算,研究了单空位缺陷对单层石墨纳米带(包括zigzag型和armchair型带)电子性质的影响.研究发现,单空位缺陷使石墨纳米带在费米面上出现一平直的缺陷态能带;单空位缺陷的引入使zigzag型半导体性的石墨纳米带变为金属性,这在能带工程中有重要的应用价值;奇数宽度的armchair型石墨纳米带表现出金属特性,有着很好的导电性能,同时,偶数宽度的armchair型石墨带虽有金属性的能带结构,但却有类似半导体的伏安特性;单空位缺陷使得奇数宽度的armchair石墨纳米带导电 关键词： 石墨纳米带 单空位缺陷 电子结构 输运性质     

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.     

全向入射条件下一维固流周期结构中低频声裂隙变化特性研究

利用传递矩阵法, 从理论上建立了全向入射条件下一维固-流周期结构中的声传播模型, 在此基础上计算、分析并比较了无限周期结构的声能带结构和有限周期结构中的声传输特性. 研究结果表明, 当声波以一定的入射角入射时, 固-流周期结构的低频通带区域存在一个声裂隙, 该声裂隙所对应的入射角大小与构成周期结构的固体层和流体层的密度或结构尺寸无关, 而仅取决于构成该周期性结构材料的波速. 关键词： 传递矩阵 全向入射 固-流周期结构 声裂隙     

Probing interlayer coupling in twisted single‐crystal bilayer graphene by Raman spectroscopy

Twisted bilayer graphene, in which interlayer interaction plays a critical role in this coupled system, is characterized for its angle‐dependent electronic and optical properties. Here, we present a systematic Raman study of single‐crystal twisted bilayer graphene grains, with the spectra of each bilayer graphene precisely correlated to its twist angle using combined transmission electron microscopic technique. Van Hove singularities develop as a result of band rehybridization at the crossing Dirac cones of the two layers, giving rise to a critical twist angle that determines the energy separation between the saddle points in the band structure and the resonance Raman spectra accordingly. The 2D mode becomes sensitive to the twist angle, showing the angle‐dependent position, peak width, and intensity. Our results interpreted in the framework of angle‐dependent double resonance scattering provide an important experimental perspective in understanding the coupled bilayer graphene system. Copyright © 2014 John Wiley & Sons, Ltd.     

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

Helmholtz resonators are widely used to reduce noise in a fluid-filled pipe system. It is a challenge to obtain lowfrequency and broadband attenuation with a small sized cavity. In this paper, the propagation of acoustic waves in a fluid-filled pipe system with periodic elastic Helmholtz resonators is studied theoretically. The resonance frequency and sound transmission loss of one unit are analyzed to validate the correctness of simplified acoustic impedance. The band structure of infinite periodic cells and sound transmission loss of finite periodic cells are calculated by the transfer matrix method and finite element software. The effects of several parameters on band gap and sound transmission loss are probed.Further, the negative bulk modulus of periodic cells with elastic Helmholtz resonators is analyzed. Numerical results show that the acoustic propagation properties in the periodic pipe, such as low frequency, broadband sound transmission, can be improved.     

Influence of different band masses on ballistic charge transport in ferromagnet–superconductor–ferromagnet trilayers

We study transport properties of clean FISIF double-barrier junctions consisting of metallic or semiconducting ferromagnets (F), a superconductor (S), and insulating interfaces (I). We solve the scattering problem based on the Bogoliubov–de Gennes equation and calculate differential conductance for arbitrary interface transparency, different effective band masses and Fermi wave vectors in the conductors. We analyze size and coherence effects that characterize ballistic transport: subgap transmission and geometrical oscillations of the conductance. We find that different band masses, as well as different Fermi wave vectors, affect the transport properties in a way similar to interfaces of a finite transparency. In all these cases, charge transport is reduced to resonant tunneling through the quasi-bound states in the superconducting film.     

Mechanically Robust,Electrically Conductive Biocomposite Films Using Antimicrobial Chitosan‐Functionalized Graphenes

An effective way of covalently functionalizing graphene with a chitosan polymer via a nitrene chemistry is demonstrated. The biofunctionalized graphene is prepared by the chemical reduction of graphene oxide using a nitrene chemistry, and then covalently grafting chitosan to the graphene surface. The effectiveness of the biofunctionalized graphene as a reinforcing filler (4 wt%) in a chitosan polymer matrix is verified by the dramatic enhancement of the mechanical properties (breaking stress = 330%, Young's modulus = 243%) and the electrical conductivity (0.3 S m^?1) without much loss in the elongation‐at‐break. The reinforcing effect can be explained by both the homogeneous dispersion of graphene within the matrix and the strong bond arising from the intrinsically intimate contact between the graphene and the matrix. The high antimicrobial activity of the biofunctionalized graphene compared with graphene oxide and chemically reduced graphene may be because of the presence of chitosan polymer on the edges of the graphene. The strong, antimicrobial graphene‐filled composite film can be used for food packaging and for coating various biomedical devices, where bacterial surface colonization is undesirable.     

Reduction of radiative transfer problems in semi-infinite media to linear Fredholm integral equations

Linear Fredholm integral equations are derived for the Stokes vector of polarized radiation, emergent from a scattering plane parallel semi-infinite medium, by means of the full range orthogonality and completeness properties of Case's eigensolutions. A renormalization concerning the eigenmode with the greatest discrete eigenvalue is applied, which permits us to obtain a new integral equation for the zeroth Fourier component of the radiation field. The kernel of the integral equations is given in terms of Case's eigenfunctions or of the Green's function matrix for an infinite medium. For isotropic scattering, it is shown that the integral equation can be solved by means of a very rapidly convergent Neumann series. Physical arguments lead to the conclusion that the renormalized Fredholm integral equations are well suited also for arbitrary phase matrices.