Expression For Density Of States Research Articles

Exactly Solvable Model Problem on a Graphene Nanoribbon with Zigzag Edges

Exact analytical expressions for the local densities of states and the occupation numbers of atoms at the zigzag edge of a graphene nanoribbon are derived in the context of a simple structural model. As an example of application of the results, the problem of a Koster–Slater defect is considered.

Giant Van Hove Density of States Singularities and Anomalies of Electron and Magnetic Properties in Cubic Lattices

Densities of states for simple (sc) and base-centered (bcc) cubic lattices with account of nearest and next-nearest neighbour hopping integrals $t$ and $t'$ are investigated in detail. It is shown that at values of $\tau \equiv t'/t = \tau_\ast$, corresponding to the change of isoenergetic surface topology, the formation of van Hove $\bf k$ lines takes place. At small deviation from these special values, the weakly dispersive spectrum in the vicinity of van Hove lines is replaced by a weak $\bf k$-dependence in the vicinity of few van Hove points which possess huge masses proportional to $|\tau - \tau_\ast|^{-1}$. The singular contributions to the density of states originating from van Hove points and lines are considered, as well as the change in the topology of isoenergetic surfaces in the $\bf k$-space with the variation of $\tau$. Closed analytical expressions for density of states as a function of energy and $\tau$ in terms of elliptic integrals, and power-law asymptotics at $\tau = \tau_\ast$ are obtained. Besides the case of sc lattice with small $\tau$ (maximum of density of states corresponds to energy level of X $\bf k$-point), maximal value of the density of states is always achieved at energies corresponding to \textit{inner} $\bf k$-points of the Brillouin zone positioned in high-symmetry directions, and not at zone faces.

Simple Models of Lateral Heterostructures

General analytical expressions for densities of states of a lateral heterostructure, formed by the contact of two square semi-infinite lattices with single-band and two-band spectra, were obtained in the tight-binding approximation by the Green’s function method. The semi-elliptical density of states was used for numerical estimates, and the model of two interacting dimers was proposed to estimate the charge transfer. Application of this approach to description of lateral epitaxial and graphene-like heterostructures is discussed.

Tachyon dynamics — for neutrinos?

Following earlier studies that provided a consistent theory of kinematics for tachyons (faster-than-light particles), we here embark on a study of tachyon dynamics, both in classical physics and in the quantum theory. Examining a general scattering process, we come to recognize that the labels given to “in” and “out” states are not Lorentz invariant for tachyons; and this lets us find a sensible interpretation of negative energy states. For statistical mechanics, as well as for scattering problems, we study what should be the proper expression for density of states for tachyons. We review the previous work on quantization of a Dirac field for tachyons and go on to expand earlier considerations of neutrinos as tachyons in the context of cosmology. We stumble into the realization that tachyon neutrinos would contribute to gravitation with the opposite sign compared to tachyon antineutrinos. This leads to the gobsmacking prediction that the Cosmic Neutrino Background, if they are indeed tachyons, might explain both phenomena of Dark Matter and Dark Energy. This theoretical study also makes contact with the anticipated results from the experiments KATRIN and PTOLEMY, which focus on beta decay and neutrino absorption by Tritium.

Простые модели латеральных гетероструктур

AbstractGeneral analytical expressions for densities of states of a lateral heterostructure, formed by the contact of two square semi-infinite lattices with single-band and two-band spectra, were obtained in the tight-binding approximation by the Green’s function method. The semi-elliptical density of states was used for numerical estimates, and the model of two interacting dimers was proposed to estimate the charge transfer. Application of this approach to description of lateral epitaxial and graphene-like heterostructures is discussed.

Solution of a torsional Schrödinger equation with a periodic potential of general form. The probability amplitude and probability density

Analytic expressions for the probability density of states of a molecule with internal rotation and the probability of finding the state in the potential well are derived for the first time. Two methods are proposed for assigning conformers to potential wells. A quantitative measure of localization and delocalization of a state in the potential well is introduced. The rotational symmetry number is generalized to the case of asymmetric rotation. On the basis of the localization criterion, a model is developed for calculating the internal rotation contribution to thermodynamic properties of individual conformers with low rotational barriers and/or at a high temperature.

Hexagonal two-dimensional layers of A N B 8–N compounds on metals

Analytical expressions for densities of states of free graphene-like A N B 8–N compounds and flat and buckled epitaxial monolayers on a metallic substrate have been obtained by the tight-binding method using a low-energy approximation. Characteristic features of the densities of states as functions of the layer–substrate coupling constant and the buckling factor have been analyzed. The energy gaps and the binding energy between the epitaxial layer and the substrate have been estimated.

Simulation of Electronic Properties of Silicon Nanotubes

Using the concepts of quantum mechanics, the atomic and electronic structure of single-layer silicon chiral nanotubes is considered. The expressions for density of states and conductivity of silicon and carbon nanotubes doped with metals are presented.

A problem on a dimer adsorbed at single-sheet graphene

In the context of the previously proposed M model for the density of states in graphene (Davydov and Sabirova [3]), two adatoms coupled via the amplitude of electron transitions from one adatom to the other (direct exchange) are considered. An analytical expression for the energy density of states in/for the dimer is derived, and the dependence of the charge of the dimer’s constituent atoms on the parameters of the problem is analyzed. The effect of image forces is investigated. In the context of the surface molecule model, a dimer composed of hydrogen adatoms is considered. The dissociation and desorption energies of such a dimer are estimated.

Theory of Electron Density of States of High Temperature Impurity Induced Anharmonic Superconductors

The expression for the electron density of states (EDOS) of high temperature superconductors (HTS) has been derived taking the disorder and anharmonicity effects as a central problem. This has been dealt with the help of double time thermodynamic Green’s function theory for electrons via a generalized Hamiltonian which consists of the contribution due to 1) unperturbed electrons; 2) unperturbed phonons; 3) isotopic impurities; 4) anharmonicities (no BCS type Hamiltonian has been taken up in the formulation); and 5) electron-phonon interactions. The renormalization effects and emergence of pairons appears as a unique feature of the theory and dependence of EDOS on impurity concentration and temperature has been discussed in details with special reference to the HTS.

Bose gas in a single-beam optical dipole trap

We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy, and Thomas-Fermi radii beyond the usual harmonic approximation.

On the microcanonical description D-brane thermodynamics

Abstract We study the microcanonical description of string gases in the presence of D-branes. We obtain exact expressions for the single string density of states and draw the regions in phase space where asymptotic approximations are valid. We are able to describe the whole range of energies including the SYM phase of the D-branes and we remark the importance of the infrared cut-off used in the high energy approximations. With the complete expression we can obtain the density of states of the multiple string gas and study its thermal properties, showing that the Hagedorn temperature is maximum for every system and there is never a phase transition whenever there is thermal contact among the strings attached to different D-branes.

Modified tight-binding equations for wave functions of semi-infinite crystals and interfaces.

An infinite set of equations for wave functions of semi-infinite crystals or interfaces in the tight-binding approximation is transformed into a finite one for coefficients of basis functions in the disturbed region and coefficients of the Bloch waves. The solutions of this set of equations permit us to construct the wave function of the whole system. The expressions for the local density of states, transmission, and reflection coefficients on the interface are obtained. As a model example the wave functions, the local densities of states, the transmission and reflection coefficients for the Pt(111) surface, treated as an interface between the crystal and empty space, are calculated for the center of the surface Brillouin zone in the linear-muffin-tin-orbital--tight-binding approximation.

On the electronic shell structure of metallic spheres and circular discs

The electronic shell structure of spherical and circular potential wells of finite depth is examined as an extension of the work of Balian and Bloch. We obtain analytical expressions for the electronic density of states, which are in good agreement with numerical results. The position of the maxima and minima in the density of states depends strongly on the depth of the potential via the quantummechanical scattering phases. For circular discs the oscillating structure in the density of states shows a different supershell pattern than for spheres. This is a consequence of the difference in the effective quantummechanical multiplicity of closed paths, which determine the oscillating structure.

Two-body density of states of hard spheres at high energies

We have extended the original formulation, given by Wentzel, for the number of bound states in a two-body potential well, to obtain an exact expression for the relative density of states. Using this expression, in the case of hard spheres, we have obtained the first three terms in an asymptotic expansion, valid at high energies and suitable for the calculation of the second virial coefficient at high temperatures.

Local density of states of a bulk Cu atom

Three expressions for the local density of states are examined. The formalism is applied to a bulk Cu atom embedded in a complex constant potential. The results for the several expressions resemble each other very well, in contrast with the results for Cu mentioned elsewhere.

Inter-band transition probabilities and photon momentum

The theory of inter-band transitions is re-examined in the case of finite photon momentumq. New expressions for the joint density of states near critical points are derived. They give Van Hove’s expressions in both the limits of long and short wavelengths. The dispersion relation for the transverse dielectric functionɛ 2T due to inter-band processes is given explicitly and it is compared to that of the longitudinal dielectric functionɛ 2L . It is shown that in the limitq = 0ɛ 2T equalsɛ 2L even for anisotropic media. The possibility of an experimental evidence of the effects caused by a finite photon momentum on the shape of the optical absorption is discussed.