Showing papers in "Physical Review B in 1985"
TL;DR: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si, suggesting a temperature-independent inherent structure underlies the liquid phase, just as for ``simple'' liquids with only pair interactions.
Abstract: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si. Implications of this potential are then explored by molecular-dynamics computer simulation, using 216 atoms with periodic boundary conditions. Starting with the diamond-structure crystal at low temperature, heating causes spontaneous nucleation and melting. The resulting liquid structurally resembles the real Si melt. By carrying out steepest-descent mappings of system configurations onto potential-energy minima, two main conclusions emerge: (1) a temperature-independent inherent structure underlies the liquid phase, just as for ``simple'' liquids with only pair interactions; (2) the Lindemann melting criterion for the crystal apparently can be supplemented by a freezing criterion for the liquid, where both involve critical values of appropriately defined mean displacements from potential minima.
4,345 citations
TL;DR: In this paper, a metal tip is scanned along the surface while ad justing its height to maintain constant vacuum tunneling current, and a contour map of the surface is generated.
Abstract: The recent development of the “scanning tunneling microscope” (STM) by Binnig et al. [8.1–5] has made possible the direct real-space imaging of surface topography. In this technique, a metal tip is scanned along the surface while ad justing its height to maintain constant vacuum tunneling current. The result is essentially a contour map of the surface. This contribution reviews the the ory [8.6–8] of STM, with illustrative examples. Because the microscopic structure of the tip is unknown, the tip wave functions are modeled as s-wave functions in the present approach [8.6, 7]. This approximation works best for small effective tip size. The tunneling current is found to be proportional to the surface local density of states (at the Fermi level), evaluated at the position of the tip. The effective resolution is roughly [2A(R+d)]1/2, where R is the effective tip radius and d is the gap distance. When applied to the 2x1 and 3x1 reconstructions of the Au(l10) surface, the theory gives excellent agreement with experiment [8.4] if a 9 A tip radius is assumed. For dealing with more complex or aperiodic surfaces, a crude but convenient calculational technique based on atom charge superposition is introduced; it reproduces the Au(l10) results reasonably well. This method is used to test the structure-sensitivity of STM. The Au(l10) image is found to be rather insensitive to the position of atoms beyond the first atomic layer.
3,192 citations
TL;DR: The dependence on channel number N of the contributions to the conductance of a small ring, periodic in the Aharonov-Bohm flux through it is obtained, and terms whose period is h/e as well as those with period h/2e vary with N as 1/N.
Abstract: The conductance of a sample scattering elastically and coupled to leads with many channels is derived. We assume that all the incident channels on one side of the sample are fed from the same chemical potential. The transmitted and reflected streams are determined by the incident streams through the multichannel scattering properties of the sample. We do not assume that the channels equilibrate with each other. Our result differs from those given earlier by other authors, except for that of Azbel [J. Phys. C 14, L225 (1981)], which is confirmed. We point out that a similar result is obtained for the conductance in a single channel at a temperature above zero. As an application, we obtain the dependence on channel number N of the contributions to the conductance of a small ring, periodic in the Aharonov-Bohm flux through it. Terms whose period is h/e as well as those with period h/2e vary with N as 1/N.
2,513 citations
TL;DR: Detailed calculations of the shift of exciton peaks are presented including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations ofexciton binding energy in a field.
Abstract: We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.
1,731 citations
PARC1
TL;DR: In this article, the authors investigated the influence of the Staebler-Wronski effect on undoped hydrogenated amorphous silicon with electron spin resonance and photoconductivity measurements.
Abstract: We study the magnitude of metastable light-induced changes in undoped hydrogenated amorphous silicon (the Staebler-Wronski effect) with electron-spin-resonance and photoconductivity measurements. The influence of the following parameters is investigated in a systematic way: sample thickness, impurity content, illumination time, light intensity, photon energy, and illumination and annealing temperatures. The experimental results can be explained quantitatively by a model based on the nonradiative recombination of photoexcited carriers as the defect-creating step. In the framework of this model, the Staebler-Wronski effect is an intrinsic, self-limiting bulk process, characterized by a strongly sublinear dependence on the total light exposure of a sample. The experimental results suggest that the metastable changes are caused by recombination-induced breaking of weak Si--Si bonds, rather than by trapping of excess carriers in already existing defects. Hydrogen could be involved in the microscopic mechanism as a stabilizing element. The main metastable defect created by prolonged illumination is the silicon dangling bond. An analysis of the annealing behavior shows that a broad distribution of metastable dangling bonds exists, characterized by a variation of the energy barrier separating the metastable state from the stable ground state between 0.9 and 1.3 eV.
990 citations
TL;DR: Theoretical arguments on the role of covalency in determining the bulk moduli of diamond and zinc-blende semiconductors and insulators are shown to yield a surprisingly simple and accurate expression for determining the Bulk Moduli B of these materials as discussed by the authors.
Abstract: Theoretical arguments on the role of covalency in determining the bulk moduli of diamond and zinc-blende semiconductors and insulators are shown to yield a surprisingly simple and accurate expression for determining the bulk moduli B of these materials. One resulting formula for compounds in the center of the Periodic Table depends only on the nearest-neighbor separation d. It has the form B=1761${d}^{\mathrm{\ensuremath{-}}3.5}$ for B in GPa and d in A\r{}.
926 citations
TL;DR: The new formulation generalizes the earlier result and draws the conclusion that there must be a symmetry breaking in the many-body ground state when applying to the fractional quantized Hall effect.
Abstract: Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by Thouless, Kohmoto, Nightingale, and den Nijs to the situation where many-body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect, we draw the conclusion that there must be a symmetry breaking in the many-body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also discussed.
822 citations
TL;DR: The method is applicable whenever the electron density of the coupled fragments does not deviate too markedly from a sum of isolated fragment densities and is particularly appropriate when full density-functional calculations are tractable for the isolated fragments but difficult for the coupled system.
Abstract: A method for calculating approximately the coupling energy of weakly interacting fragments is presented. The method is a simplified version of the density-functional scheme of Kohn and Sham and is applicable whenever the electron density of the coupled fragments does not deviate too markedly from a sum of isolated fragment densities. The coupling energy is expressed directly in terms of properties of the isolated fragments and the only nontrivial computational step is the determination of an eigenvalue sum for the coupled system with a fixed potential. Neither self-consistency cycling nor a solution of Poisson's equation for the coupled fragments is required. The method is therefore particularly appropriate when full density-functional calculations are tractable for the isolated fragments but difficult for the coupled system, e.g., a molecule interacting with a surface. Explicit calculations for dimers illustrate that the approach is very accurate for weakly interacting systems, and that reasonable results can be obtained even for strong covalent bonds.
769 citations
TL;DR: The two-dimensional Hubbard model on a square lattice with nearest-neighbor hopping is studied and it is suggested that the system is always paramagnetic, in contradiction with Hartree-Fock predictions.
Abstract: We have studied the two-dimensional Hubbard model on a square lattice with nearest-neighbor hopping. We first discuss the properties of the model within the mean-field approximation: Because of the form of the band structure, some peculiar features are found. We then discuss the simulation algorithm used and compare simulation results with exact results for 6-site chains to test the reliability of the approach. We present results for thermodynamic properties and correlation functions for lattices up to 8\ifmmode\times\else\texttimes\fi{}8 in spatial size. The system is found to be an antiferromagnetic insulator for all values of the coupling constant at zero temperature in the half-filled-band case, but the long-range order is much smaller than predicted by mean-field theory. We perform a finite-size-scaling analysis to determine the character of the transition at zero coupling. For non-half-filled-band cases, our results suggest that the system is always paramagnetic, in contradiction with Hartree-Fock predictions. The system does not show tendency to ferromagnetism nor triplet superconductivity in the parameter range studied. We also discuss some properties of the attractive Hubbard model in the half-filled-band case.
721 citations
TL;DR: Asymptotically exact results for the charge and spin densities far away from finite systems (atoms and molecules) and far outside solid surfaces are derived and it is shown that the uppermost DF eigenvalue in each spin channel is also given by exact excitation energies.
Abstract: We derive asymptotically exact results for the charge and spin densities far away from finite systems (atoms and molecules) and far outside solid surfaces. These results are then used to obtain the correct asymptotic form of the exchange-correlation potential of density-functional (DF) theory and to prove that, for all systems, the eigenvalue of the uppermost occupied DF orbital equals the exact ionization potential. For spin-polarized finite systems we show that the uppermost DF eigenvalue in each spin channel is also given by exact excitation energies.
697 citations
TL;DR: Using a flexible version of a rigid-molecule model of water, the velocity autocorrelation functions are analyzed to investigate the effect of the liquid milieu on the high-frequency internal modes of molecular motion.
Abstract: Using a flexible version of a rigid-molecule model of water we have analyzed the velocity autocorrelation functions to investigate the effect of the liquid milieu on the high-frequency internal modes of molecular motion. The calculations have been made at 1 g ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and at 250, 325, and 375 K. Good agreement with experimentally determined pair correlations has also been found.
TL;DR: In this article, the effects of an exciton gas and an electron-hole plasma on the excitonic optical absorption in a two-dimensional semiconductor and compare these with recent experimental results on absorption saturation in single and multiple-quantum-well structures.
Abstract: We present theoretical results for the effects of an exciton gas and an electron-hole plasma on the excitonic optical absorption in a two-dimensional semiconductor and compare these with recent experimental results on absorption saturation in single- and multiple-quantum-well structures. A simple theoretical description of the nonlinear optical properties of these microstructures is developed for the case of low-density optical excitation near and above the band edge. We argue that the effects of Coulomb screening of excitons by the plasma are relatively weak in these structures but that the consequences of phase-space filling and exchange are significant in each case. We are able to explain the recent unexpected experimental result that ``cold'' excitons are more effective than ``hot'' carriers in saturating the excitonic absorption. Good agreement with the experimental data is obtained without adjustable parameters.
TL;DR: In this paper, the authors measured and calculated the 3d (${M}_{4}$5) absorption spectra for all the rare-earth metals, as well as the full 3d −4f multiplets for the early and late rare earths.
Abstract: We have measured and calculated the 3d (${M}_{4}$,5) absorption spectra for all the rare-earth metals, as well as the full 3${d}^{9}$4${f}^{n+1}$ multiplets for the early and late rare earths. The quality of agreement between theory and experiment is excellent, except for Sm. In x-ray-absorption spectroscopy (XAS), only dipole selected lines are seen but all multiplet effects can be observed in x-ray photoemission spectroscopy. The line shapes and 3d-4f interactions are discussed. Our results provide an improved basis for use of the 3d XAS spectra for studies of ``mixed-valence'' systems.
TL;DR: A simple modification of a standard pseudopotential generation scheme is developed, and the new, smoother potentials are shown to decay significantly faster in reciprocal space, with no loss of transferability.
Abstract: Modern norm-conserving pseudopotentials are constructed to satisfy a set of criteria for the matching of pseudo- and all-electron eigenvalues and wave functions. In practice, it is also desirable that they be as smooth as possible, so that their reciprocal-space representation decays as quickly as possible. To this end, a simple modification of a standard pseudopotential generation scheme is developed. The new, smoother potentials are shown to decay significantly faster in reciprocal space, with no loss of transferability.
TL;DR: Various features of quasicrystal diffraction patterns are discussed and the projection scheme is used throughout and applied in some detail to the pattern formed by icosahedral Al-Mn.
Abstract: Various features of quasicrystal diffraction patterns are discussed. The projection scheme is used throughout and applied in some detail to the pattern formed by icosahedral Al-Mn. Comparison with the diffraction pattern formed by the vertices of a three-dimensional Penrose tiling leads to the value 4.60 A\r{} for the rhombohedron edge length.
PARC1
TL;DR: In this article, the stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems, and explicit forms of the stress field within the local density approximation are given, together with a generalization of the approximate Liberman form for pressure.
Abstract: The stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. Stress fields are considered in two alternative forms, both of which give the same macroscopic stress and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the stress field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.
TL;DR: The spectral properties of the HRTEM roughness on normally prepared and intentionally roughened samples appears to be well characterized as a first-order autoregressive or Markovian process which corresponds to an exponential decay in the autocovariance function rather than the usual Gaussian approximation which has been widely used.
Abstract: We have studied the statistical properties of random surface roughness at the Si-${\mathrm{SiO}}_{2}$ interface using high-resolution transmission electron microscopy (HRTEM). The spectral properties of the HRTEM roughness on normally prepared and intentionally roughened samples appears to be well characterized as a first-order autoregressive or Markovian process which corresponds to an exponential decay in the autocovariance function rather than the usual Gaussian approximation which has been widely used. Such an exponential decay is characterized by tails in the spectrum which are directly attributable to the discrete or steplike nature of the interface roughness which is restricted to occur on crystalline atomic sites. Using a simplified model, we have estimated the effect of projecting the two-dimensional interface roughness through the cross-section thickness to form the one-dimensional boundary studied here. For an isotropic medium, we find that the statistical character of the roughness is preserved during this transformation, but that the rms fluctuation of the roughness is attenuated so that the actual interface is rougher than indicated by the HRTEM technique. After correcting for such averaging, the parameters estimated from the HRTEM are more in agreement with the same parameters used to fit the surface-roughness-limited Hall mobility in metal-oxide-semiconductor field-effect transistor devices.
TL;DR: The dynamic scaling hypothesis and finite-size scaling explain well the observed temperature and size dependence of the data, and the functional form of the correlation functions is com- patible with the scaling form if corrections to scaling are taken into account.
Abstract: I present an analysis of the dynamic behavior of short-range Ising spin glasses observed in stochastic simulations. The time dependence of the order parameter q(t)=〈${S}_{x}$(0)${S}_{x}$(t)〉\ifmmode\bar\else\textasciimacron\fi{}---which is the same as that of the structure factor---and the time dependence of the related dynamic correlation functions have been recorded with good statistics and very long observation times. The spin-glass model with a symmetric distribution of discrete nearest-neighbor \ifmmode\pm\else\textpm\fi{}J interactions on a simple-cubic lattice was used. Simulations were performed with a special fast computer, allowing for the first-time investigation of the equilibrium dynamics for a wide range of temperatures (0.7\ensuremath{\le}kT/J\ensuremath{\le}5.0) and lattice sizes (${8}^{3}$, ${16}^{3}$, ${32}^{3}$, and ${64}^{3}$). I have found that the empirical formula q(t)=${\mathrm{ct}}^{\mathrm{\ensuremath{-}}x}$exp(-\ensuremath{\omega}${t}^{\ensuremath{\beta}}$) with temperature-dependent exponents x(T) and \ensuremath{\beta}(T) describes the decay very well at all temperatures above the spin-glass transition. In the spin-glass phase, only the algebraic decay q(t)=${\mathrm{ct}}^{\mathrm{\ensuremath{-}}x}$ could be observed, with different temperature dependences of the exponent x(T). The dynamic scaling hypothesis and finite-size scaling explain well the observed temperature and size dependence of the data, and the functional form of the correlation functions is com- patible with the scaling form if corrections to scaling are taken into account. The scaling behavior and the dynamic and static critical exponents found in my simulations are in reasonable agreement with recent experiments performed on insulating spin glasses, showing that despite its simplicity the discrete model of spin glasses analyzed in this work displays behavior similar to that seen in nature.
TL;DR: The possibility of ellipsoidal distortions in free-electron metal clusters, analogous to the shape variations among atomic nuclei, was investigated with the use of a modified Nilsson Hamiltonian as discussed by the authors.
Abstract: The possibility of ellipsoidal distortions in free-electron metal clusters, analogous to the shape variations among atomic nuclei, is investigated with the use of a modified Nilsson Hamiltonian. In most cases, the predicted equilibrium shape is ellipsoidal rather than spherical, so that the spherical shells are divided into ellipsoidal subshells. A strong correlation is observed between the energy-level sequence of these subshells and the sequence of peaks in alkali-metal cluster mass spectra, indicating that metal clusters generally assume approximately ellipsoidal shapes.
IBM1
TL;DR: La diffusion directe de la lumiere par les modes acoustiques guides thermiquement excites d'une fibre optique constitue une source de bruit thermique.
Abstract: Forward light scattering by the thermally excited guided acoustic modes of an optical fiber produce numerous narrow lines not predicted by the usual theory of Brillouin scattering. Optical heterodyne detection has been used to resolve the scattering spectrum which begins at about 20 MHz and extends to the detection limit. A simple theory quantitatively accounts for the frequencies, polarizations, and intensities of the components. The light scattering from these modes constitutes a thermal-noise source in optical fibers that may prove significant in other experiments.
TL;DR: The dynamical behavior of arbitrarily configured, interacting quantized vortex filaments is investigated by means of numerical experiments and analytical estimates and an analytical depinning criterion involving both normal and superfluid velocities is derived, and found to be in good agreement with the numerical experiments.
Abstract: The dynamical behavior of arbitrarily configured, interacting quantized vortex filaments is investigated by means of numerical experiments and analytical estimates. Several prototype situations of interest in the theory of superfluid turbulence and critical velocities are considered. It is shown that if a vortex loop approaches a surface to within a critical distance, a localized cusplike deformation is generated which drives the vortex into the surface at a well-defined point. If the vortex is reconnected to the surface in this limit, the two ends which now terminate on the surface quickly move apart. The entire process can be well approximated by making a simple reconnection at the critical distance. A similar process is found to occur when two vortex filaments try to cross, with two cusps developing which bring the lines together at a point in such a way that a line-line reconnection naturally ensues. More complicated versions of the reconnection process occur when a vortex terminates on a flat surface which contains a pinning site in the form of a local protrusion. Such a vortex is captured by the pinning site when it approaches to within a critical distance. Once a vortex is pinned, it requires a finite flow velocitymore » to free it from the pinning site. At the depinning velocity, the vortex reconnects to the flat surface and moves off. An analytical depinning criterion involving both normal and superfluid velocities is derived, and found to be in good agreement with the numerical experiments.« less
TL;DR: The surface composition of Ni-Cu alloys has been calculated as a function of atomic layer, crystal face, and bulk composition at a temperature of 800 K and the results show that the composition varies nonmonotonically near the surface with the surface layer strongly enriched in Cu while the near-surface layers are enriched in Ni.
Abstract: The surface composition of Ni-Cu alloys has been calculated as a function of atomic layer, crystal face, and bulk composition at a temperature of 800 K. The results show that the composition varies nonmonotonically near the surface with the surface layer strongly enriched in Cu while the near-surface layers are enriched in Ni. The calculations use the embedded-atom method [M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)] in conjunction with Monte Carlo computer simulations. The embedding functions and pair interactions needed to describe Ni-Cu alloys are developed and applied to the calculation of bulk energies, lattice constants, and short-range order. The heats of segregation are computed for the dilute limit, and the composition profile is obtained for the (100), (110), and (111) surfaces for a variety of bulk compositions. The results are found to be in accord with experimental data.
PARC1
TL;DR: In this paper, the authors presented explicit formulas for the calculation of stress based on the stress theorem and the local density-functional approximation for calculations on the semiconductors Si, Ge, and GaAs.
Abstract: Explicit formulas for the calculation of stress are presented based on the stress theorem and the local-density-functional approximation. Norm-conserving pseudopotentials are applied in a plane-wave basis for calculations on the semiconductors Si, Ge, and GaAs. Besides the lattice constants and bulk moduli, complete sets of elastic constants are given, together with the optical \ensuremath{\Gamma} phonon frequencies and internal-strain parameter \ensuremath{\zeta}. Electronic charge density structure factors, deformation potentials, and strain-induced splittings of phonons are given, as well as the nonlinear third-order elastic constants. Good agreement with experiment is found throughout, except for persistent deviations from the x-ray diffraction values for \ensuremath{\zeta}.
TL;DR: Raman scattering studies of a variety of (GaAl)As superlattices grown by molecular-beam epitaxy are presented in this article, where folded acoustic phonons appear as doublets in the Raman spectra.
Abstract: Raman scattering studies of a variety of (GaAl)As superlattices grown by molecular-beam epitaxy are presented. Folded acoustic phonons appear as doublets in the Raman spectra. Their frequencies are accurately predicted by several models, including an approximate solution of an elastic continuum model through a perturbation approach. Scattering intensities of the folded acoustic modes are predicted by a photoelastic continuum model. Calculations on a layered dielectric continuum provide information about anisotropy of optical phonons. Linear-chain model calculations indicate that optical phonons in binary superlattices are largely confined to alternate layers. Peaks in the Raman data are identified with the resulting quantized optic modes. It is shown that Raman scattering has the potential to provide structural information similar to that which can be obtained by x-ray diffraction.
TL;DR: It is shown that the width of the ``optic peak'' increases roughly linearly with the rms bond-angle distortion of the network, consistent with model-building experience which shows that it is impossible to construct fully bonded amorphous networks with \ensuremath{\Delta}${\ensureMath{\theta}}_{b}$.
Abstract: The Raman scattering from various model structures for amorphous silicon is computed. It is shown that the width of the ``optic peak'' increases roughly linearly with the rms bond-angle distortion \ensuremath{\Delta}${\ensuremath{\theta}}_{b}$ of the network. The experimentally observed linewidths lead to 7.7\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\Delta}${\ensuremath{\theta}}_{b}$\ensuremath{\le}10.5\ifmmode^\circ\else\textdegree\fi{}. The smaller linewidths (and hence angles) correspond to networks that have been annealed at higher temperatures. These results are consistent with model-building experience which shows that it is impossible to construct fully bonded amorphous networks with \ensuremath{\Delta}${\ensuremath{\theta}}_{b}$\ensuremath{\le}6.6\ifmmode^\circ\else\textdegree\fi{}.
TL;DR: It is concluded that only a self-consistent theory like the TDLDA (or an improvement of it) is able to account for all the complexity of the electronic response in small dimensions.
Abstract: The dynamical electronic response properties of small metal particles are calculated within the frame of the self-consistent spherical jellium model. The method used is the TDLDA (time-dependent local-density approximation) with the inclusion of exchange and correlation. In this way we obtain for the first time insight into the nonlocal electronic response properties at a strictly microscopic level. The size dependence of photoabsorption, photoemission, and of the static polarizability, is discussed in detail. The emergence of the collective volume mode (the volume plasmon) as a function of the numbers of electrons is shown here for the first time. Likewise, the size-dependent Landau damping of these modes is obtained in a quantitative fashion. Compared with the results of any non-self-consistent model, we conclude that only a self-consistent theory like the TDLDA (or an improvement of it) is able to account for all the complexity of the electronic response in small dimensions.
TL;DR: In this paper, the scaling behavior of sliding charge-density waves is analyzed in terms of a classical description of impurity pinning, with emphasis on the behavior near threshold considered as a dynamic critical phenomenon.
Abstract: The dynamic properties of sliding charge-density waves are discussed in terms of a classical description of impurity pinning, with emphasis on the behavior near threshold considered as a dynamic critical phenomenon. A mean-field model introduced previously [Phys. Rev. Lett. 50, 1486 (1983)] is analyzed in detail, including ac response above and below threshold and hysteretic behavior below threshold. For short-range interactions, the weak-pinning limit is discussed and scaling behavior is predicted near threshold. The earlier prediction of ac noise with intensity inversely proportional to the square root of the volume with a diverging amplitude near threshold caused by a diverging correlation length is analyzed in terms of the scaling behavior; this interpretation of the noise is semiquantitatively confirmed by recent experiments of Mozurkewich and Gr\"uner [Phys. Rev. Lett. 51\ensuremath{\rightarrow}, 2206 (1983)]. Many of the ideas presented here may be applicable to other systems, especially weakly pinned flux flow in type-II superconductors.
TL;DR: In this article, it was shown that the coherency strain generated by lattice mismatch dramatically reduces the indirect gap of the alloy, which approaches the gap of unstrained Ge at 0.75.
Abstract: Estimates of the indirect band gap for coherently strained alloys of ${\mathrm{Ge}}_{\mathrm{x}}$${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ on Si〈001〉 are given for x in the range 0\ensuremath{\le}x\ensuremath{\le}0.75. The present results were obtained by combining x-ray diffraction data with relevant deformation-potential constants and using the phenomenological strain Hamiltonian of Kleiner and Roth. Uniaxial splittings of the sixfold-degenerate valence-band edge were calculated using the 6\ifmmode\times\else\texttimes\fi{}6 Hamiltonian of Hasegawa. It is found that the coherency strain generated by lattice mismatch dramatically reduces the indirect gap of the alloy (which approaches the ${L}_{1}$-${\ensuremath{\Gamma}}_{25}^{\mathcal{'}}$ gap of unstrained Ge at x\ensuremath{\simeq}0.6).