Influence of internal degrees of freedom on the structure of one-dimensional systems

Summary The influence of internal degrees of freedom on the behaviour of one-dimensional systems is discussed. For systems with half-filled bands the coupling to internalviz. lattice coordinates decides whether Peierls distortion is caused by intramonomer coordinates or by a lattice coordinate. Thereby the various intramonomer degrees of freedom act cooperatively. We show that there is a small regime of parameters where both kinds of distortion exist simultaneously. For increasing temperature we find that distortions can also move from the lattice coordinate to the intramonomer coordinate.     

Temperature dependent energy bands and the metal-nonmetal transition in NiS

The LCMTO (linear combination of muffin-tin orbitals) technique has been used to calculate the first temperature dependent energy bands for a transtion metal compound. The particular compound studied was hexagonal NiS which undergoes a first-order metal-to-nonmetal transition as the temperature is lowered below 264K. We find the bands to agree well with XPS data and that the Sp bands overlap the bottom of the d bands as predicted by White and Mott. This p-d overlap, which reduces the correlation energy, is found to increase with temperature as a result of lattice vibrations whereas the lattice distortion accompanying the transition has very little effect on the energy bands. This suggests that the Mott-Hubbard transition in NiS is driven by the Debye-Waller modification of the potential and not the lattice distortion as suggested by White and Mott.     

Lattice electrons on a cylinder surface in the presence of rational magnetic flux and disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.     

Bloch oscillations and Zener tunneling in two-dimensional photonic lattices

We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap spectrum.     

Response function of coarsening systems

We calculate analytically the conditions that establish the number of bound states in finite superlattices as a function of the depth, width and separation of the wells. We consider a lattice of -wells and a set of rectangular wells. For this latter case, we show how for finite systems the energy levels already group together in bands separated by gaps. Received 24 April 1998     

双氮协同钴掺杂锐钛矿相二氧化钛电子结构的第一性原理研究

采用基于密度泛函理论的第一性原理计算了双氮原子协同钴原子共掺杂TiO2的几何结构和电子结构. 计算结果发现: 双氮原子掺杂引起的双空穴位与钴原子形成了较强的耦合作用, 并引起晶格结构发生明显变化. 共掺杂的协同效应引起TiO2禁带宽度变窄,在价带顶和导带底出现大量杂质能级, 从而引起吸收带边发生明显红移. 该掺杂方式对调制TiO2禁带宽度有明显的效果, 有望指导后续的实验合成.     

Flat bands and Wigner crystallization in the honeycomb optical lattice

We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.     

Lawless Universe: Science and the Hunt for Reality

The four chief features to be expected in the infra-red absorption spectrum of a semiconductor are :—the intrinsic edge, lattice bands, impurity bands, and free carrier absorption. The first two of these, which have been explored with high resolution, are discussed in detail. Measurements of the absorption spectrum near the intrinsic edge in germanium and silicon show that indirect transitions take place, and that ‘excitons’ are formed; and the intrinsic energy gap can be deduced accurately. The lattice bands yield the main features of the lattice vibration spectrum.     

Photonic band structure in the nearly plane wave approximation

For photons propagating in a periodic dielectric lattice, the dispersion curve forms photonic bands separated by forbidden gaps. When the dielectric lattice deviates only slightly from being homogenous, the photonic band structure resembles the linear dispersion relation for photons folded into the first Brillouin zone, i.e., the so-called empty lattice bands. Using group theoretical technique, we calculate the splitting of the accidental degeneracies in the empty lattice bands at symmetry points for a simple cubic dielectric lattice. Received 23 June 1998     

格点QCD中有限体积下形状因子的内插计算

在格点QCD的框架下,讨论了计算强子的形状因子的过程中,有限体积效应对所得结果的影响,并且给出了计算连续动量空间上形状因子数值的内插算法.本文以π介子的形状因子为例,介绍了从格点QCD中得到的三点关联函数出发计算π介子的形状因子的方法,并说明有限体积效应使得计算结果只能在分立动量上给出.本文探讨了一种保持旋转对称性的内...     

X‐ray diffractometry and topography of lattice plane curvature in thermally deformed Si wafer

The correlation between the microscopic lattice plane curvature and the dislocation structure in thermal warpage of 200 mm‐diameter Czochralski Si (001) wafers has been investigated using high‐resolution X‐ray diffractometry and topography. It is found that the (004) lattice plane curvature is locally confined between two neighboring slip bands, with the rotation axis parallel to the slip bands. High‐resolution topography reveals that the curvature resulted from a fragmented dislocation structure. The local confinement is attributed to the multiplication of the dislocations that are generated between the two slip bands.     

Killing the Hofstadter butterfly,one bond at a time

Electronic bands in a square lattice when subjected to a perpendicular magnetic field form the Hofstadter butterfly pattern. We study the evolution of this pattern as a function of bond percolation disorder (removal or dilution of lattice bonds). With increasing concentration of the bonds removed, the butterfly pattern gets smoothly decimated. However, in this process of decimation, bands develop interesting characteristics and features. For example, in the high disorder limit, some butterfly-like pattern still persists even as most of the states are localized. We also analyze, in the low disorder limit, the effect of percolation on wavefunctions (using inverse participation ratios) and on band gaps in the spectrum. We explain and provide the reasons behind many of the key features in our results by analyzing small clusters and finite size rings. Furthermore, we study the effect of bond dilution on transverse conductivity (σ _xy ). We show that starting from the clean limit, increasing disorder reduces σ _xy to zero, even though the strength of percolation is smaller than the classical percolation threshold. This shows that the system undergoes a direct transition from a integer quantum Hall state to a localized Anderson insulator beyond a critical value of bond dilution. We further find that the energy bands close to the band edge are more stable to disorder than at the band center. To arrive at these results we use the coupling matrix approach to calculate Chern numbers for disordered systems. We point out the relevance of these results to signatures in magneto-oscillations.     

Optical properties of radical cation salts derived from the TTF molecule: Evidence for electronic correlations and phase transitions in organic conductors

Following a general presentation of the organic conductors which belong to the series of radical cation salts derived from the tetrathiafulvalene molecule we analyze the characteristic charge transfer absorption bands observed in these mixed valence compounds. Using a Drude-Lorentz model we show that the energy gap present in these materials is basically of the Hubbard type. Nevertheless we observe also in specific cases additional contributions due to either a periodic lattice distortion or a counter-ion electrostatic perturbation. We conclude finally that the electronic correlations are the dominant interactions in these narrow 1d electronic band systems.     

The Electronic and Lattice Structures of the Groundand the Polaron States of Polymer Poly (Phenylene Vinylene) (PPV)

The electronic and lattice structures of poly (phenylene vinylene) (PPV) are studied theoretically. Both the electron-electron and electron-phonon interactions are taken into account in the Pariser-Parr-Pople model. The electronic band and the lattice structure of the ground state and the polaronic state are calculated by means of the unrestricted Hartree-Fock method. In the ground state, there exist eight bands in PPV including four valence bands and four conduction bands, and the benzenes can be considered to be rigid. The polaron induces the split of energy bands. There are four localized electronic states within the energy gap. The defect of the polaron appears to extend over about 5 units. The benzenes are strongly affected by the electron-phonon interaction. Our calculation for the energy band structure of the ground and polaron states are consistent with experimental absorption spectra. The results of our calculation show that the electron-phonon and inter-site electron-electron interactions play an important role in determining the electronic and lattice structures.     

The Electronic and Lattice Structures of the Ground and the Polaron States of Polymer Poly (Phenylene Vinylene) (PPV)

The electronic and lattice structures of poly (phenylene vinylene) (PPV) are studied theoretically. Both the electron-electron and electron-phonon interactions are taken into account in the Pariser-Parr-Pople model. The electronic band and the lattice structure of the ground state and the polaronic state are calculated by means of the unrestricted Hartree-Fock method. In the ground state, there exist eight bands in PPV including four valence bands and four conduction bands, and the benzenes can be considered to be rigid. The polaron induces the split of energy bands. There are four localized electronic states within the energy gap. The defect of the polaron appears to extend over about 5 units. The benzenes are strongly affected by the electron-phonon interaction. Our calculation for the energy band structure of the ground and polaron states are consistent with experimental absorption spectra. The results of our calculation show that the electron-phonon and inter-site electron-electron interactions play an important role in determining the electronic and lattice structures.     

Analytical design of photonic band-gap fibers and their dispersion characteristics

The paper essentially deals with the analysis of photonic band-gap fibers in analogy with the electron wave motion in periodic crystal lattice. As such, the analyses are based on Bloch formulation. The dispersion characteristics of such fibers are presented by considering some illustrative values of design parameters. The effect of design parameters on the dispersion characteristics is also presented in terms of the variation of widths of allowed and forbidden bands of band-gap fibers. It is found that the number of allowed bands increases with the increase in difference between refractive indices of different layers. Further, widths of the allowed and forbidden bands increase with the increase in layer thickness.     

A honeycomb lattice model simulating the surface states of topological insulators

A honeycomb lattice model exhibiting the quantum spin-Hall effect is proposed, where the low-energy properties of the electrons are mainly determined by the energy spectrum in the vicinity of the Γ point, for suitable parameters. The nontrivial topology of the energy bands is revealed by calculating the Chern numbers, Berry curvature distribution, and edge state spectrum. We further show that in the continuum limit, the model Hamiltonian is equivalent to the effective model for the surface states in thin films of three-dimensional topological insulators. As a consequence, this lattice model provides a useful tool for numerical simulation of the physical properties of the surface states.     

Brillouin zone unfolding of complex bands in a nearest neighbour tight binding scheme

Complex bands k(⊥)(E) in a semiconductor crystal, along a general direction n, can be computed by casting Schr?dinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice vectors, the order of this eigenvalue problem can grow large for arbitrary n. It is, however, possible to always choose a set of non-primitive lattice vectors such that the eigenvalue problem is restricted to be quadratic. The complex bands so obtained need to be unfolded onto the primitive Brillouin zone. In this paper, we present a unified method to unfold real and complex bands. Our method ensures that the measure associated with the projections of the non-primary wavefunction onto all candidate primary wavefunctions is invariant with respect to the energy E.     

Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

Cathodoluminescence of ZnS single crystals subjected to thermal annealing in vapors of the constituents

The 77°K cathodoluminescence spectra of ZnS single crystals grown from the melt and annealed in vapors of the constituents were studied in the spectral region 360 to 550 nm. The single crystals contained oxygen whose phase state could be changed by thermal annealing. The effect of oxygen in the ZnS lattice on the appearance and intensities of various bands in the zinc sulfide spectrum was investigated. It turned out that the bands at 390–400 nm, 410–430 nm, and 500–525 nm are associated with the luminescence of a solid solution of ZnS· O in the lattice. The intensity of the green luminescence was a function of oxygen concentration in precipitates of the solid solution on dislocations. The luminescence in the 363 to 370 nm region is associated with zinc oxide which separates from ZnS containing various amounts of sulfur.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 84–88, May, 1975.