Quantum size effects in the fermi energy and electronic density of states in a finite square well thin film model

The dependence of the Fermi energy, E_F, and the electronic density of states, ρ(E), of thin metallic films (L_z ≲ 50 Å) on film thickness, electron density, and potential well depth, is systematically investigated in a free-electron, finite square well model. Two size-dependent effects are observed: (1) oscillations in E_F and ρ(E) due to the size-quantization of the energy levels, and (2) changes in the mean values of these quantities, averaged over several oscillation periods, relative to their bulk values. The mean value of E_F is increased relative to its bulk value by as much as 5%–10% for physically reasonable well depths and typical metallic electron densities. For the special case in which the top energy level in the well is occupied, the mean value of E_F is equal to its bulk value. The mean value ofρ(E_F) can be either greater than or less than its bulk value, depending on the well depth. In contrast to the small amplitude oscillations in E_F, the oscillations in ρ(E_F) may have an amplitude as large as 25% of the mean value for sufficiently thin films. Accurate analytic expressions for the thickness dependence of the Fermi energy and density of states are derived.     

Periodic boundary conditions for a 1d disordered system: Influence on the density of states and the shape of the wavefunctions

For a special one-dimensional disordered system which allows a particularly transparent investigation of the kind of problem in question, we study how the density of states and the detailed shape of the wavefunctions are influenced by changing the boundary conditions imposed on the system.The spatial propagation of the wavefunctions is treated within the framework of the transfer matrix method. Periodic boundary conditions only become possible if we do not fix the value of the wavefunctions at the edges of the system. They induce a certain correlation between the random sequence characterizing the disordered system and the space dependence of the wavefunctions. The existence of this kind of correlation then leads to an argument which, although not rigorous, makes localization of almost all states in the usual sense highly unplausible for periodic boundary conditions.     

Influence of isolated para-hydrogen molecules in solid ortho-hydrogen on the libron density of states

A Green function theory is used to calculate the influence of isolated para-hydrogen defects in solid hydrogen on the libron density of states. Librons are treated within the harmonic approximation (RPA).Extract from D 26     

The density of states at the fermi level of the non-crystalline semiconductors

Conclusion On the basis of our experimental results on glassy As₂Te₃ we have shown that the results on the films of As₂Te₃, concerning the conductivity _F (approximately linearly rising with the frequency) and the following density of states at the Fermi level are affected mainly by the thin film nature of samples.The estimated value of the density of statesG(E _F ) at the Fermi level for glassy As₂Te₃ isG(E _F ) 10¹⁸ eV^–1 cm^–3 which is no longer in contradiction with the other results.     

Fluctuations in the level density of a fermi gas

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many-body density of states, related to shell effects, are obtained. The fluctuations depend nontrivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single-particle motion.     

Effects of boundary conditions on spatially periodic states

We investigate analytically and numerically the influence of linear homogeneous boundary conditions on the stationary solutions of a simple model for cellular pattern formation in one dimension. For all boundary conditions there exists in a reduced wavenumber band at least one static solution where the amplitude falls below its bulk value near the boundary (“Type-I” solution). A linear stability analysis of the uniform state at threshold reveals that Type-I solutions are often unstable. Then there exists in the full Eckhaus-stable band, a static solution where the amplitude rises above its bulk value near the boundary (“Type-II” solution), or a limit-cycle solution where the amplitude near the boundary oscillates. These solutions bifurcate from the homogeneous state below the bulk threshold and therefore remain finite at threshold.     

Local density of states of one-dimensional Mott insulators and charge-density wave states with a boundary

We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.     

固体物理教学中电子态密度的计算

电子态密度是指单位能量范围内的状态数,是与电子能带结构密切相关的一个物理量.为了计算电子的比热和晶体的输运性质,必须用较精确的方法计算出晶体的电子态密度.大多数教材中对该部分的处理通常采用简化模型,并不能反映一般情况下态密度的计算思路.本文从电子态密度的公式出发,详细说明了二维石墨烯和三维面心立方晶格态密度的计算步骤,并且对其中细节给出了基于数值计算的详细解释.     

Influence of thermal boundary conditions on the double-diffusive process in a binary mixture

This paper presents a precise numerical simulation of the transport processes in a rectangular cavity saturated with a binary liquid mixture. The full transient Navier-Stokes equations coupled with the mass and heat transfer equations are solved, numerically, using the finite-volume method. After validation against a proven commercial code comparing solutions on a benchmark natural convection problem, the newly developed code is used for a series of numerical experiments. Realistic thermal boundary conditions have been chosen, and the more drastic situation of power loss while conducting the experiment in microgravity is considered. The molecular and thermal diffusion coefficients are computed from theoretical models. Results reveal that, when vertical walls are held at constant but different temperatures, species separate in both the longitudinal and the transverse directions as radiation is allowed to take place along the horizontal walls. The numerical experiments performed clearly demonstrate that the kinetics of the mass transport in the mixture are conditioned by the ability to monitor the heat sources properly. Specifically, sudden temperature changes strongly disturb species separation in the experimental cells. This paper provides some trends for the accurate analysis of experiments involving mass transport inasmuch as the convective level is low enough to allow evaluation of the transport coefficients.     

广义边界条件和概率流密度的连续性

以四参量族－广义边界条件代替有限深方势阱内粒子波函数的对数的一阶导数连续性条件，表明这种替换比用广义边界条件取代一盒子内自由粒子波函数在两壁处为零的边界条件显行更加合理些。我们发现，如对参量ρ和θ取任意值，则会导致概率流密度连续性被破坏。我们找到了约束ρ和θ取值的条件，并得到一组新的解析解。     

An approximate scheme to determine the vibratory density of states in a quasi-harmonic solid

In a new and realistic conception of solids, an analytical approach is presented to find the phonon density of states in a quasi-harmonic one-dimensional solid by starting from the fact that a solid with strong interatomic forces can be regarded as an atomic array of quantum anharmonic oscillators under a Morse potential. In fact, our quasi-harmonic approximation is derived by assuming a large enough solid with an involved anharmonic parameter as a sufficiently small quantity. In this context, a mathematical relationship between the above parameter and the matrix element relative to oscillator’s strength is obtained.     

Remote two-time boundary conditions and special states in quantum mechanics

For an oscillating universe, the assumptions of wave-function localization and approximate symmetry for the initial and final states impose restrictions on the intermediate motion. We argue that one of these restrictions is the avoidance of superpositions of macroscopically distinct states.     

Influence of the charge concentration on the density of states in a two-dimensional superconducting system

The gap and the density of states of high-T_c superconductors have been a subject of paramount interest. In order to explain the observed experimental behavior several pairing mechanisms in high-temperature superconductivity have been considered, by theoretical calculations. In this work, within the BCS scheme, a two-band model with energy band overlapping is introduced. The gap parameter and the density of states in a two-dimensional superconducting system are studied as functions of the charge concentration. This model is applied to Bi2212 in order to obtain numerical results.     

Boundary energy and boundary states in integrable quantum field theories

We study the ground-state energy of integrable 1 + 1 quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new “R-channel TBA”, where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic field, and also results for the energy, excited states and boundary S-matrix of O(n) and minimal models.     

Effects of atomic size on antiphase boundary energy in solid solutions

The energy of an antiphase boundary has been calculated by means of Pines's elastic spheres method, as modified by incorporating the dependence of atomic size on the neighbors in the first coordination sphere, which represents an advance in the theory of ordered solid solutions. There is a reduction in the elastic strain energy when a nonequilibrium antiphase boundary is formed in CuZn, and if this is incorporated one obtains realistic values for the energies of such boundaries; in AuCu₃ the elastic strain energy increases the energy of an antiphase boundary of octahedral type. The change in the elastic strain energy in a nonequilibrium antiphase boundary constitutes a considerable part of the total energy change given by the quasichemical theory, and it introduces substantial corrections into the antiphase-boundary energy for CuZn and AuCu₃.     

Appearance conditions for a semiconducting-substrate-induced gap in the density of states in epitaxial graphene

The density of states in a semiconducting substrate is described with a model assuming a parabolic electronic spectrum. Analytical criteria for the appearance of a gap (gaps) in the density of states in epitaxial graphene are derived, and its (their) parameters (width and position relative to the forbidden gap of the substrate) are found. A way to experimentally verify analytical data is suggested.     

Influence of the boundary conditions on the thermostimulated depolarization current

Thermally stimulated depolarization currents (TSD) are analyzed as a function of conditions on the contacts (within the framework of blocking and unblocking the electrodes). It is shown that in the case of the blocking electrodes the TSD can be due to resorption of the volume charge, neutralization of the volume charge because of equilibrium conduction, and repolarization in the internal field. In the case of the unblocking electrodes, the TSD depends substantially on the electrical neutrality of the object. The influence of the diffusion component of the conduction current on the TSD current is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 7–13, December, 1979.