Average Density Of States Research Articles

Systematics of the average resonance widths in overlapping resonance-scattering and its connection with RRKM theory

Decay processes of densely distributed quasi-bound states are studied numerically by randomly generating the Hamiltonian matrices. The average decay rate obtained from the Feshbach theory of resonance scattering exhibits systematic behavior against the average density of states (ρ), the number of continua ( K) and the average coupling strength to the continua (υ). The distribution of the decay rates bifurcates into long-lived and short-lived branches when ρ is larger than a certain critical value ρ c, which is found to be roughly equal to the inverse of the 0-th order partial width 〈γ part〉. Thus one can clearly distinguish the isolated resonance regime in the region ρ<ρ c and overlapping resonance regime in the region ρ⪢ρ c. The states belonging to the short-lived branch exhibit a very broad energy spectrum and are recognized as background continua. They are not quasi-bound states in practice. The decay rates of the long-lived branch, on the other hand, systematically decrease with ρ at ρ ⪢ ρ c. The average of these decay rates is proportional to 〈γ part〉 −1 Kρ −2. When the short-lived branch is excluded, the average decay rate, 〈Γ/ℏ〉, roughly agrees with that of the RRKM rate in the region ρ ≈ ρ c, where the spectral profile becomes most diffuse. Outside the region of ρ ≈ ρ c, 〈Γ/ℏ〉 is always smaller than the RRKM rate. The above observation is confirmed also by a square-we potential model and ascertains the conventional belief that the RRKM theory holds only when resonances overlap and that it gives the upper bound. It is noteworthy that this RRKM regime corresponds to the critical overlap, ρ〈γ part.〉 ≈ 1.

Theoretical analysis of pure effects of strain and quantum confinement on differential gain in InGaAsP/lnP strained-layer quantum-well lasers

The pure effects of both strain and quantum confinement on differential gain of InGaAsP/InP strained-layer quantum-well lasers (SL-QWL's) are studied on the basis of valence band structures calculated by k/spl middot/p theory. Using an InGaAsP quaternary compound as an active layer makes it possible to distinguish the effect of strain (both tensile and compressive) from the quantum-confinement effect when keeping the emission wavelength constant. The essential features of strain-induced changes in the valence band structures are extracted from the k/spl middot/p results by four characterization parameters: the averaged density of states (DOS), the subband energy spacings, the joint density of electron and hole states, and the squared optical matrix elements. Each of them is then directly correlated to differential gain in SL-QWL's. In tensile-strained quantum wells, all of these factors are significantly improved compared with unstrained wells, while only the averaged DOS is improved in compressive-strained wells. Due to these characteristic features, it is concluded that the intrinsic potential of tensile-strained QWL's for improving differential gain is twice as high as that of compressive-strained ones. On the basis of the essential features of the strain-induced changes in valence band structures, we also discuss basic design principles for SL QWL's with larger differential gain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Density of states for band random matrices with electric field

We present a long-range hopping tight-binding model in which the ensemble averaged density of states, rho (E), undergoes a gradual transition from a homogeneous form with almost no variation to strongly peaked behaviour as an external electric field grows. The model consists of N*N band random matrices of bandwidth b. The corresponding matrix elements, hij, have all vanishing average except on the diagonal where, (hii)= alpha i. Here, the parameter alpha plays the role of the electric field. We approximate the behaviour of the width, sigma E, of the local density of states, rho L(E), and use it to predict the value of alpha around which the transition is centred.

Motion of a quantum particle in a random-flux field.

We consider a charged spinless quantum particle moving on a two-dimensional square lattice. Each plaquette of the lattice is penetrated by a random magnetic flux with values homogeneously distributed in the interval (0, 2π) (in units of the elementary quantum flux h/e). The fluxes in different plaquettes are statistically independent. With the path integral method, within the saddle-point approximation, we evaluated the averaged density of states. Our results are compared with the recent numerical-simulation predictions of Pryor and Zee

Electronic properties of one-dimensional quasiperiodic lattices: Green's function renormalization group approach

Using the inflation-deflation symmetry, we have developed a new real-space decimation approach to study the electronic properties of one-dimensional quasiperiodic lattices. The key result is the construction of a compact renormalization group that allows simple calculation of the average Green's function and the average density of states to any degree. The Fibonacci and the generalized Fibonacci lattices are used to demonstrate the method. Numerical results for the average density of states of these lattices show a good agreement with the results obtained by other methods. This confirms the validity and the efficiency of the approach.

Shell structure and level spacing distribution in metallic clusters

The lattice gas Monte Carlo and tight binding method is used to study the electronic shell structure in large metallic clusters. The average density of states of a large ensemble of deformed clusters shows the same shell structure as the most spherical geometry. The level spacing distribution at the Fermi level is a Wigner distribution.

A numerical study of sparse random matrices

A numerical study is presented for the eigensolution statistics of largeN×N real and symmetric sparse random matrices as a function of the mean numberp of nonzero elements per row. The model shows classical percolation and quantum localization transitions atp c =1 andp q >1, respectively. In the rigid limitp=N we demonstrate that the averaged density of states follows the Wigner semicircle law and the corresponding nearest energy-level-spacing distribution functionP(S) obeys the Wigner surmise. In the very sparse matrix limitp≪N, withp>p q a singularity 〈ρ(E))∝1/¦E¦ is found as¦E¦→ 0 and exponential tails develop in the high-¦E¦ regions, but theP(S) distribution remains consistent with level repulsion. The localization properties of the model are examined by studying both the eigenvector amplitude and the density fluctuations. The valuep q 1.4 is roughly estimated, in agreement with previous studies of the Anderson transition in dilute Bethe lattices.

Electronic Structure of Generalized Fibonacci Lattices. I.Invariant, Quasi-Invariant and Cyclic Orbits

Dynamical trace-map of the tight-binding model is investigated by generalizing the stacking rule of the Fibonacci lattice. The recurrence relation is defined by D ( n +1)= D ( n ) p D ( n -1) q for positive integers p and q , where D ( n ) is the atomic sequence of the n -th generation. The structure of the dynamical trace-map is analyzed in terms of the invariant and the quasi-invariant of the map. Characteristic features of the wave function, local density of states and the average density of states are analyzed.

Exact results on Landau-level broadening

For an electron in the plane subjected to a perpendicular constant magnetic field and a homogeneous random potential the authors investigate the averaged density of states restricted to an arbitrary Landau level They calculate the exact width for an arbitrary random potential. For general Gaussian random potentials they prove the existence of Gaussian tails and determine the decay constants. Furthermore, they derive Jensen-type lower and upper bounds to expectation values of convex functions with respect to the restricted density of states. Using similar bounds they estimate the effect of Landau-level mixing.

Generalized Fibonacci lattice dynamical trace map, invariant and quasi-invariant

Dynamical trace map of the tight-binding model is investigated for the generalized Fibonacci lattice characterized by the stacking rule S( n+1)= S( n) p S( n−1) q with p,q integers, where S(n) is the atomic sequence of the n-th generation. An expression is found of a quasi-invariant which is valid for any set of (p,q) and also of the invariant of the trace map for q=1 and q= p+1. Average density of states is calculated for p=2, q=1, 2 and 3.

Electronic structure of amorphous silicon carbide compounds

Abstract The electronic structure of a-Si1–x Cx, has been calculated for the whole range of C concentrations (0 ⩽x ⩽1). The atomic structure of the alloy has been modelled by an ideal continuous random network in which some Si-C atomic correlations have been considered. The electronic levels have been obtained from a nearest-neighbour tight-binding Hamiltonian that has been solved within the Bethe lattice and effective-medium approximations. The gap increase that follows C incorporation is correctly reproduced by our calculations up to x values close to 0·7. The employed structural model based on fourfold coordination of both Si and C atomic species loses its validity for higher C contents. Besides average densities of states, other electronic magnitudes of physical interest such as joint densities of states, spectral and optical gaps, valence and conduction band edges, and energy levels of defect states produced by Si and C dangling bonds have been obtained. We have extended the definition of the charge ...

Aspects of landau-level broadening using the path integral representation

With the help of Wiener-type path integrals we accomplish a systematic study of two different, previously proposed versions of a first-order cumulant approximation to the averaged density of states for an electron in two dimensions under the influence of a perpendicular homogeneous magnetic field and a homogeneous isotropic random potential. Explicit results are given for a Gaussian random potential with a Gaussian covariance function.

Electron states in disordered layers

The authors discuss the application of the first-principles Korringa-Kohn-Rostoker coherent potential approximation to the calculation of the electronic structure of substitutionally disordered alloys with layer geometries (surfaces, interfaces etc)-the LKKRCPA. The canonical problem of this type is that of a single layer of a random binary alloy, and they present results for a Cu0.5Pd0.5 monolayer. They compare the effective scattering amplitudes and average densities of states with those of the bulk FCC alloy, and comment on the significance of the result for the surface electronic structure of Cu-Pd alloys. They outline how disordered layers may be embedded onto or between bulk substrates in order to treat real alloy surfaces or interfaces.

Correspondence principles: the relationship between classical trajectories and quantum spectral

The general correspondence principle specifies a relationship between wave functions and families of trajectories. For bounded systems with regular trajectories, this general correspondence principle leads to the principle of quantization of action. The general principle also leads to a correspondence principle for finite-resolution spectra: oscillation in the average density of states, or in the average oscillator strength as a function of energy, are connected to periodic or to closed orbits. This principle holds independently or whether classical trajectories are orderly or chaotic.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the Landau-level broadening by deltaor constantly correlated random potentials

For the averaged density of states of non-interacting electrons in an infinite plane subject to a perpendicular uniform magnetic field and a delta-correlated random potential a scaling relation is obtained by using Feynman path integrals. As an example we rederive the density of states of the Landau-Lloyd model, give a closed-form expression and show that the absence of level mixing is a general property of the Cauchy-Lorentzian randomness. The latter is also true for constantly correlated randomness with an arbitrary single-site distribution.

Nature of the eigenstates on a Fibonacci chain.

We have studied the nature of the eigenstates on a Fibonacci chain. A careful study of the averaged density of states reveals a highly structured density. We have also studied the eigenfunctions at the band center and find that the charge density as well as a quantity related to the entropy of the eigenfunctions possess the same fractal dimension.

An extended recursion method for the calculation of average density of states

The authors describe an extended recursion method that allows direct calculation of the average density of states and that possesses the numerical stability of the recursion scheme. They show the relation between the extended recursion and the moments methods.

Electronic structure of amorphousSi3N4in the cluster-Bethe-lattice approximation

We present a calculation of the electronic structure of amorphous ${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$, using a model tight-binding Hamiltonian with a basis set of Si 3s and 3p, and N 2s and 2p orbitals. Clusters of 13 atoms, centered at either a Si or a N atom, are constructed using structural data from crystalline \ensuremath{\beta}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$. These clusters are employed to generate a self-consistent transfer-matrix approximation for an infinite effective medium (Bethe lattice). The local and average densities of states are evaluated using standard one-particle Green's operator techniques. We also simulate photoemission spectra by weighting orbitally decomposed partial densities of states with appropriate photoemission cross sections. Our results are in good agreement with recent experimental data.

Electronic structure of copper-rich copper-palladium alloys

In considering the electronic structure of (Cu-rich) $\mathrm{Cu}\mathrm{Pd}$ alloys, we present computations of complex-energy bands and average densities of states together with the angle-resolved photoemission spectra from the (100), (111), and (110) surfaces of ${\mathrm{Cu}}_{95}$${\mathrm{Pd}}_{5}$ and ${\mathrm{Cu}}_{85}$${\mathrm{Pd}}_{15}$ single crystals. The impurity spectrum in $\mathrm{Cu}\mathrm{Pd}$ is found to be dominated by two quite-well-separated Pd-derived impurity bands and differs sharply from the case of $\mathrm{Cu}\mathrm{Ni}$ or $\mathrm{Ag}\mathrm{Pd}$ systems, where only a single Ni- or Pd-related impurity structure appears in the alloy. Extensive comparisons between the theory and experiment are carried out with regard to the positions and halfwidths of the Pd-induced impurity structures, the level shifts and disorder smearings of the Cu-derived bands, and the shifts in the binding energies of the $\mathrm{Cu}2p$ and $\mathrm{Pd}3d$ core levels. A remarkably good agreement is found to exist in all cases. The (111) Shockley state is observed to lie at a binding energy of 0.2 eV (with respect to the Fermi energy) in ${\mathrm{Cu}}_{95}$${\mathrm{Pd}}_{5}$ and to possess an increased full width at half maximum (compared to Cu) of 60 meV. This state moves just above the Fermi energy in ${\mathrm{Cu}}_{85}$${\mathrm{Pd}}_{15}$. These effects can also be understood in terms of the changes in the bulk electronic spectrum of Cu upon alloying with Pd.

Structure-Induced Minimum in the Average Spectrum of a Liquid or Amorphous Metal

Nonperturbative multiple-scattering theory is used to study the influence of the first peak in the density correlation function, $s(k)$, on the electronic properties of a structurally disordered metal. The present calculations yield a well-defined minimum in the average density of states and a corresponding peak in the electrical resistivity. The position of these structures is directly related to that of the principal peak in $s(k)$.