# Showing papers in "Physical Review B in 1970"

••

IBM

^{1}TL;DR: In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering by the external surfaces.

Abstract: In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering due to the external surfaces. The intrinsic or bulk resistivity is obtained by solving a Boltzmann equation in which both grain-boundary and background scattering are accounted for. The total resistivity is obtained by imposing boundary conditions due to the external surfaces (as in the Fuchs theory) on this Boltzmann equation. Interpretation of published data on grain-boundary scattering in bulk materials in terms of the calculated intrinsic resistivity, and of thin-film data in terms of the calculated total resistivity suggests that (i) the grain-boundary reflection coefficient in Al is \ensuremath{\approx} 0.15, while it is somewhat higher in Cu; (ii) the observed thickness dependence of the resistivity in thin films is due to grain-boundary scattering as well as to the Fuchs size effect; and (iii) the common observation that single-crystal films possess lower resistivities than polycrystalline films may be accounted for by grain-boundary effects rather than by differences in the nature of surface scattering.

1,720 citations

••

TL;DR: In this paper, the theory of the inhomogeneous electron gas, with local exchange and correlation energies, was used to obtain self-consistent electron density distributions and the surface energy was found to be negative for high densities, and the resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al).

Abstract: The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron gas, with local exchange and correlation energies, is used. Self-consistent electron density distributions are obtained. The surface energy is found to be negative for high densities (${\mathcal{r}}_{s}\ensuremath{\le}2.5$). In the second part, two corrections to the surface energy are calculated which arise when the positive background model is replaced by a pseudopotential model of the ions. One correction is a cleavage energy of a classical neutralized lattice, the other an interaction energy of the pseudopotentials with the electrons. Both of these corrections are essential at higher densities (${\mathcal{r}}_{s}\ensuremath{\le}4$). The resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagreement.

1,260 citations

••

1,039 citations

••

Bell Labs

^{1}TL;DR: In this article, a simple phenomenological theory of the elastic constants of sphalerite structure crystals is presented and shown to apply within reasonable errors to the known experimental constants, including the shear constants which decrease markedly with ionicity.

Abstract: A simple phenomenological theory of the elastic constants of sphalerite structure crystals is presented and shown to apply within reasonable errors to the known experimental constants. The theory utilizes a form for bond-stretching ($\ensuremath{\alpha}$) and bending ($\ensuremath{\beta}$) forces first used by Keating, to which are added effective point-ion Coulombic forces. Also it is pointed out that regularities in the experimental elastic constants of these crystals are readily explained in terms of the ionicity ${f}_{i}$ defined by Phillips and Van Vechten. Of particular note are the shear constants which decrease markedly with ionicity. It is found that this decrease is described quantitatively by $\frac{\ensuremath{\beta}}{\ensuremath{\alpha}}\ensuremath{\propto}(1\ensuremath{-}{f}_{i})$, which confirms the interpretation of $\ensuremath{\beta}$, since bond-bending forces should vanish in the ionic limit ${f}_{i}\ensuremath{\rightarrow}1$. Other equally simple formulas for the forces in terms of only the bond length and ${f}_{i}$ are shown to predict all the constants with a rms accuracy of 10%.

931 citations

••

TL;DR: In this paper, it was shown that by using alternate layers of materials with high and low elastic constants resolved shearing stresses of the order of ε( √ n ϵ(n 2 ) −1 −1/n −1 )$ will be required in order to drive dislocations through the combination.

Abstract: It is shown that by using alternate layers of materials with high and low elastic constants resolved shearing stresses of the order of $\frac{{\ensuremath{\mu}}_{\mathrm{low}}}{100}$ will be required in order to drive dislocations through the combination. The layers should be so thin that a Frank Read source cannot operate inside one layer. The low-elastic-constant material should be such that perfect dislocations rather than partials occur in bulk specimens of the material. Several possible combinations are suggested.

884 citations

••

TL;DR: In this paper, the main Hall-effect mechanism was shown to be the main mechanism for the dc Hall effect for Fe, Ni, and their alloys above 100 K, while asymmetric scattering dominates below 100 K.

Abstract: The center of mass of a wave packet undergoes a discontinuous and finite sideways displacement on scattering by a central potential, in the presence of spin-orbit interaction. This is the main Hall-effect mechanism (${\ensuremath{\rho}}_{H}\ensuremath{\propto}{\ensuremath{\rho}}^{2}$) for Fe, Ni, and their alloys above 100 K, while asymmetric scattering dominates below 100 K. Displacement $\ensuremath{\Delta}y$ per actual collision is calculated by partial waves. In the case of Born expansion, the leading term of $\ensuremath{\Delta}y or \frac{{\ensuremath{\rho}}_{H}}{{\ensuremath{\rho}}^{2}}$ is of zero order in the scattering potential. The magnitude is predicted correctly ($\ensuremath{\Delta}y\ensuremath{\approx}{10}^{\ensuremath{-}10}\ensuremath{-}{10}^{\ensuremath{-}11}$ m) when using the effective spin-orbit Hamiltonian derived by Fivaz from spin-orbit interband mixing. The calculation of ${\ensuremath{\rho}}_{H}$ is extended to arbitrary ${\ensuremath{\omega}}_{c}\ensuremath{\tau}$ for compensated and un-compensated metals. Other nonclassical physical mechanisms proposed by Karplus and Luttinger and by Doniach and by Fivaz are spurious for the dc Hall effect.

877 citations

••

Bell Labs

^{1}TL;DR: In this article, it was shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom.

Abstract: It is shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom. The susceptibility and effective mass are calculated in the metallic phase and are found to be enhanced by a common factor which diverges at the critical value of the interaction.

820 citations

••

754 citations

••

TL;DR: In this paper, a unified treatment for phonon sideband intensities, multiphonon relaxation transition probabilities, and phonon-assisted energy-transfer probabilities is given in the adiabatic approximation.

Abstract: A unified treatment is given in the adiabatic approximation for phonon sideband intensities, multiphonon relaxation transition probabilities, and phonon-assisted energy-transfer probabilities. The intensity distribution of phonon sidebands is determined by coupling constants of the vibrational modes with electrons or holes and a criterion for the appearance of discrete sidebands is given. Transition probabilities of multiphonon relaxation processes among various excited levels of an ion are shown to depend exponentially on the energy gap between these levels, in agreement with recent experimental results. A similar dependence is derived for the energy-transfer probabilities between two ions on the energy mismatch between excitation energies of these ions.

726 citations

••

TL;DR: In this paper, a model for determining the density of states of pure stoichiometric NiO is proposed, taking into account the free-ion energy levels, and taking the Madelung potential, screening and covalency effects, crystalline-field stabilizations, and overlap effects.

Abstract: The electrical and optical properties of materials which are characterized by narrow bands in the vicinity of the Fermi energy are discussed. For such materials, electronic correlations and the electron-phonon coupling must be considered explicitly. Correlations in $f$ bands and in extremely narrow $d$ bands can be handled in the ionic limit of the Hubbard Hamiltonian. It is shown that free carriers in such bands form small polarons which contribute to conduction only by means of thermally activated hopping. Wider bands may also exist near the Fermi energy. Carriers in these bands may form large polarons and give a bandlike contribution to conductivity. A model is proposed for determining the density of states of pure stoichiometric crystals, beginning with the free-ion energy levels, and taking into account the Madelung potential, screening and covalency effects, crystalline-field stabilizations, and overlap effects. Exciton states are considered explicitly. The Franck-Condon principle necessitates the construction of different densities of states for electrical conductivity and optical absorption. Because of the bulk of experimental data presently available, the model is applied primarily to NiO. The many-particle density of states of pure stoichiometric NiO is calculated and is shown to be in agreement with the available experimental data. When impurities are present or nonstoichiometry exists, additional transitions must be discussed from first principles. The case of Li-doped NiO is discussed in detail. The calculations are consistent with the large mass of experimental information on this material. It is concluded that the predominant mechanism for conduction between 200 and 1000 \ifmmode^\circ\else\textdegree\fi{}K is the transport of hole-like large polarons in the oxygen $2p$ band. A method for representing the many-particle density of states on an effective one-electron diagram is discussed. It is shown that if correlations are important, donor or acceptor levels cannot be drawn as localized levels in the energy gap when multiple conduction or valence bands are present. This result comes about because extrinsic ionization energies of two correlated bands differ by an energy which bears no simple relation to the difference in energies of the intrinsic excitations, which are conventionally used to determine the relative positions of the bands.

698 citations

••

TL;DR: In this paper, a variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local energy procedure or alternately as a numerical integration scheme.

Abstract: A general variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local-energy procedure or alternately as a numerical integration scheme. This rapidly convergent procedure circumvents many of the difficulties associated with the evaluation of matrix elements of the Hamiltonian in an arbitrary basis and treats the general nonspherical potential with no more complication than the usual "muffin-tin" approximation. Thus the band structure of ionic and covalent materials can be calculated with realistic crystal potentials. As an example, the method is applied to the one-electron model Hamiltonian with a nonspherical local potential, using a linear combination of atomic orbitals basis. Matrix elements of the Hamiltonian are evaluated directly without decomposition into atomic basis integrals; no "tight-binding" approximations are made. Detailed calculations are presented for the band structure and charge density of bcc lithium which demonstrate the feasibility of our method, and reveal the sensitivity of the energy bands to nonspherical and exchange components of the crystal potential. Various prescriptions for the construction of crystal potentials are considered, and convenient least-squares expansions are described. The extension of these methods to nonlocal potentials such as are encountered in the Hartree-Fock self-consistent-field procedure is discussed.

••

TL;DR: In this paper, the first and second-order Raman spectra of diamond were studied using the 4880 and 5145 lines of an Ar ion laser and the 6328 \AA{} line of a He-Ne laser.

Abstract: The first- and second-order Raman spectra of diamond were studied using the 4880 \AA{} and 5145 \AA{} lines of an Ar ion laser and the 6328 \AA{} line of a He-Ne laser. The spectra were recorded at room, liquid-nitrogen, and liquid-helium temperatures. In addition to the second-order spectrum previously reported by Krishnan, a new weaker second-order spectrum was observed in the range 1600-2100 ${\mathrm{cm}}^{\ensuremath{-}1}$. Polarization studies were carried out on both the first- and second-order spectra. From such studies it was established that the 1332-${\mathrm{cm}}^{\ensuremath{-}1}$ Raman line is the zone-center optical phonon with ${\ensuremath{\Gamma}}^{(25+)}$ (${F}_{2g}$) symmetry. The prominent features in both the second-order Raman spectra reported here and the second-order infrared spectra are interpreted in terms of the critical points of the phonon dispersion curves established from neutron spectroscopy and on the basis of space-group selection rules.

••

Hitachi

^{1}TL;DR: In this paper, a determination is made of all possible species of full ferromagnetic, partial ferromagnetics, full ferroelectrics, partial magnetization vector, spontaneous polarization vector, or spontaneous strain tensor, and it is found out in which of these species two or all of the three types should couple completely or incompletely with each other.

Abstract: A ferromagnetic, ferroelectric, or ferroelastic crystal is called full or partial, according to whether all or not all but some of its orientation states are different in spontaneous magnetization vector, spontaneous polarization vector, or spontaneous strain tensor. In previous theories \char22{} for nonmagnetic crystals \char22{} the concept of "species" was introduced, a determination was made of all possible species of full ferroelectrics and of full ferroelastics, and those species were found in which ferroelectricity and ferroelasticity coexist and completely couple with each other. These theories are now extended to cover magnetic crystals in addition to nonmagnetic crystals and to cover the partial in addition to the full. A determination is made of all possible species of full ferromagnetics, partial ferromagnetics, full ferroelectrics, partial ferroelectrics, full ferroelastics, and partial ferroelastics, and it is found out in which of these species two or all of ferromagnetism, ferroelectricity, and ferroelasticity should couple completely or incompletely with each other.

••

TL;DR: In this article, the temperature dependence of the elastic stiffness constants was investigated for 57 elastic constants of 22 substances and the applicability of these two equations and that of Wachtman's equation was examined.

Abstract: The following two equations are proposed for the temperature dependence of the elastic stiffness constants: ${c}_{\mathrm{ij}}={c}_{\mathrm{ij}}^{0}\ensuremath{-}\frac{s}{({e}^{\frac{t}{T}}\ensuremath{-}1)}$ and ${c}_{\mathrm{ij}}=a\ensuremath{-}\frac{b{T}^{2}}{(T+c)}$, where ${c}_{\mathrm{ij}}^{0}$, $s$, $t$, $a$, $b$, and $c$ are constants. The applicability of these two equations and that of Wachtman's equation is examined for 57 elastic constants of 22 substances. The first equation has a theoretical justification and gives the best over-all results. Neither of the three equations give the theoretically expected ${T}^{4}$ dependence at low temperatures, and therefore they are not expected to give very accurate results at very low temperatures ($\ensuremath{\lesssim}\frac{{\ensuremath{\Theta}}_{D}}{50}$). A new melting criterion is also examined.

••

IBM

^{1}TL;DR: In this article, photoelectric work functions of polycrystalline films of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Y, Zr, Nb, Mo, Pd, Ag, La, Ce, Nd, Sm, Eu, Gd, Hf, Pt, and Au are reported.

Abstract: Photoelectric work functions of polycrystalline films of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Y, Zr, Nb, Mo, Pd, Ag, La, Ce, Nd, Sm, Eu, Gd, Hf, Pt, and Au are reported.

••

TL;DR: In this paper, the problem of the band structure of semiconductor alloy systems is treated by both the dielectric two-band method and by the use of an empirical (local) pseudopotential.

Abstract: The problem of the band structure of semiconductor alloy systems is treated by both the dielectric two-band method and by the use of an empirical (local) pseudopotential. With both methods, calculations are made in the virtual-crystal approximation assuming linear dependence on alloy concentration of the lattice constant and the parameters of the two methods. Contrary to some previous assertions, both methods predict, in general, a nonlinear dependence of the interband gaps on concentration. An estimate is also made of the effects of second-order perturbations to the virtual-crystal approximation, i.e., the effect of disorder. Of particular interest are the lowest direct and indirect energy gaps and the deviations of these from linearity. The treatment is confined to alloys of compounds having the formula ${A}^{N}{B}^{8\ensuremath{-}N}$, but quaternary and more complicated alloys may be treated as easily as the ternary alloys to which most previous experimental work has been confined. Results are compared to experiment and to the empirical formula of Thompson and Woolley. We find that, with one free parameter, the dielectric method gives good agreement with experiment, but that the local-pseudopotential method apparently does not yield satisfactory results for this problem.

••

TL;DR: In this article, the Born-von Karman force constants in an arbitrary solid, crystalline or amorphous, are derived in terms of the complete inverse dielectric function of the electrons.

Abstract: The microscopic quantum-mechanical expressions for the Born-von Karman force constants in an arbitrary solid, crystalline or amorphous, are derived in terms of the complete inverse dielectric function ${\ensuremath{\epsilon}}^{\ensuremath{-}1}(\mathrm{r}, {\mathrm{r}}^{\ensuremath{'}})$ of the electrons The many-body nature of the electrons is treated exactly; only the Born-Oppenheimer approximation is made. Born's translation and rotation invariance conditions are shown to be satisfied by the microscopic force constants. In the case of a perfect crystal, it is shown for the first time that the microscopic formulas recapture completely the phenomenological form of the dynamical matrix; in particular, the microscopic expression for the effective charge in an insulator is found. We prove that the charge neutrality of the system implies the "effective charge neutrality" condition and that, consequently, all acoustic-mode frequencies vanish at long wavelength. This condition may be stated as a useful property of ${\ensuremath{\epsilon}}^{\ensuremath{-}1}$ which we term the acoustic sum rule. Many results of the phenomenological theory, e.g., the generalized Lyddane-Sachs-Teller relation, carry over exactly to the microscopic theory.

••

TL;DR: In this article, the authors measured the linewidth and the frequency of the q = 0 optical phonon in silicon over the temperature range of 20-770, and deduced an absolute halfwidth of 2.1

Abstract: We have measured the linewidth and the frequency of the q=0 optical phonon in silicon over the temperature range of 20-770\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependence of the linewidth has been interpreted as arising from the decay of the optical phonon to two LA phonons at half the optical frequency. From the observed temperature variation, we deduce an absolute half-width $\ensuremath{\Gamma}$ of 2.1 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 0\ifmmode^\circ\else\textdegree\fi{}K. This value is considerably smaller than that obtained theoretically by Cowley on the basis of numerical calculations which include decay to phonons throughout the Brillouin zone. His numerical calculations also predict a temperature dependence of the linewidth which does not agree with experiment. However, the observed change in frequency with temperature correlates very well with Cowley's theory. We have also studied the relative intensities of Stokes and anti-Stokes components of Raman spectra. The observed temperature dependence of the relative intensities is compared with that predicted on the basis of the Bose-Einstein population factor for the optical phonon.

••

••

Bell Labs

^{1}TL;DR: In this paper, the density of states and the mobility of an extra electron or hole are calculated in the atomic limit of the Hubbard model in terms of the number of paths which return to the origin leaving the spin configuration unchanged.

Abstract: In this paper, the density of states and the mobility of an extra electron or hole are calculated in the atomic limit of the Hubbard model. Both the half-filled single-band and multiple-band situations are discussed. The problem is formulated in terms of the number of paths which return to the origin leaving the spin configuration unchanged. The density of states then depends on spin configuration and we have considered the random (R) (high-temperature) and antiferromagnetic (AF) arrangements. Examination of the first five nonzero moments for the simple cubic lattice indicates that the bands are narrowed by a factor of 0.745 (AF) and 0.805 (R). However, the exact bands have tails extending out to the full free-particle width for both spin arrangements. An approximate one-particle Green's function is obtained by summing all graphs with no closed loops. Such paths give a density of states that is independent of spin arrangement and is relatively flat with a sharp square-root edge at $2{(z\ensuremath{-}1)}^{\frac{1}{2}}t$. Here $z$ is the coordination number and $t$ is the nearest-neighbor hopping integral. Within this approximation, we have calculated the mobility of an extra hole and have found typical values to be \ensuremath{\sim}1 ${\mathrm{cm}}^{2}$/V sec so that the mobility is rather small, even though the density of states has a width of order \ensuremath{\sim}1 eV. Intra-atomic exchange is shown to give a further narrowing of the band [a factor of ${(2)}^{\ensuremath{-}1/2}$ in the two-band large-intra-atomic-exchange example]. The effect of finite $\frac{t}{U}$ is considered, where $U$ is the intra-atomic Coulomb interaction, and is shown to have a strong effect on the band tail but relatively weak effects on the bulk of the band. Finally, we make a few remarks comparing our results with the observed mobilities in NiO and the relevance of intra-atomic exchange to the behavior of the dioxide and sesquioxide series.

••

TL;DR: In this article, the optical reflectance spectra of the transition-metal oxides NiO and CoO have been measured over the energy range from 1 to 26 eV.

Abstract: The optical reflectance spectra of the transition-metal oxides NiO and CoO have been measured over the energy range from 1 to 26 eV. The optical constants have been derived by means of a Kramers-Kr\"onig analysis of their reflectance spectra. Structure in reflectance is found at 4.0, 4.8, 5.9, 7.2, 8.25, 12.8, 13.6, and 17.8 eV in NiO, and at 5.5, 7.5, 12.6, and 17.5 eV in CoO. The positions of high-energy structure in their absorption coefficients is consistent with maxima in their respective optical densities of states determined from photoemission data. Two alternative interpretations are given for the structure in NiO between 4.0 and 9.0 eV. One interpretation involves oxygen $p$ and nickel $d$ states in localized excitations, and the other involves the nickel $d$ states and the "$4s$" band. Distinction between models on the basis of presently available photoconductivity data is found to be questionable.

••

Bell Labs

^{1}TL;DR: In this paper, a model based upon a time-dependent Ginzburg-Landau equation was proposed to obtain a new estimate of ε-Omega$ which is different in functional form from the LA estimate, and smaller than that estimate by more than 10 orders of magnitude for the conditions in recent experiments.

Abstract: A thermal-activation theory of intrinsic fluctuations in thin superconducting wires has been proposed by Langer and Ambegaokar (LA). Their fluctuation rate equals an exponential activation factor ${e}^{\ensuremath{-}\frac{\ensuremath{\Delta}F}{{k}_{B}T}}$ times a prefactor $\ensuremath{\Omega}$ which fixes the fluctuation time scale. Using a model based upon a time-dependent Ginzburg-Landau equation, we obtain a new estimate of $\ensuremath{\Omega}$ which is different in functional form from the LA estimate, and smaller than that estimate by more than 10 orders of magnitude for the conditions in recent experiments. To within corrections which are roughly of order unity, our expression is $\ensuremath{\Omega}=(\frac{L}{\ensuremath{\xi}})\frac{{(\frac{\ensuremath{\Delta}F}{{k}_{B}T})}^{\frac{1}{2}}}{\ensuremath{\tau}}$, where ($\frac{L}{\ensuremath{\xi}}$) is the length of the sample in units of the Ginzburg-Landau coherence length $\ensuremath{\xi}$, ${(\frac{\ensuremath{\Delta}F}{{k}_{B}T})}^{\frac{1}{2}}$ is a correction for overlap of fluctuations at different places along the wire, and $\ensuremath{\tau}\ensuremath{\approx}{10}^{\ensuremath{-}8}$ sec is the relaxation time in the Ginzburg-Landau equation. Although our specific expressions have been derived from a time-dependent Ginzburg-Landau theory, we expect from general physical arguments that they are relatively insensitive to the starting model.

••

Bell Labs

^{1}TL;DR: In this paper, the simplest Kondo problem is treated exactly in the ferromagnetic case, and given exact bounds for the relevant physical properties in the antiferromagnetic cases, by use of a scaling technique on an asymptotically exact expression for the ground-state properties given earlier.

Abstract: The simplest Kondo problem is treated exactly in the ferromagnetic case, and given exact bounds for the relevant physical properties in the antiferromagnetic case, by use of a scaling technique on an asymptotically exact expression for the ground-state properties given earlier. The theory also solves the $n=2$ case of the one-dimensional Ising problem. The ferromagnetic case has a finite spin, while the antiferromagnetic case has no truly singular $T\ensuremath{\rightarrow}0$ properties (e.g., it has finite $\ensuremath{\chi}$).

••

TL;DR: In this paper, the optical absorption coefficient for direct, excitonic transitions in a uniform applied electric field is calculated and the electron-hole scattering is treated within the effective mass approximation and leads to an absorption coefficient which differs markedly in size and shape from the Franz-Keldysh absorption spectrum.

Abstract: Numerical calculations of the optical-absorption coefficient for direct, excitonic transitions in a uniform applied electric field are presented. The electron-hole scattering is treated within the effective-mass approximation and leads to an absorption coefficient which differs markedly in size and shape from the Franz-Keldysh absorption spectrum. A detailed numerical study of the shape of the absorption-edge spectrum at photon energies somewhat below the zero-field absorption threshold suggests that for small field strengths the dominant asymptotic form of the absorption coefficient is $\mathrm{exp}(\ensuremath{-}\frac{{C}_{0}|E\ensuremath{-}{{E}_{0}}^{\ensuremath{'}}|}{f})$, where $f=\frac{|e|\mathrm{Fa}}{R}$ is the electric field strength in units of exciton Rydbergs per electron-exciton Bohr radius. This result contradicts the existing belief that the electron-hole interaction does not alter the asymptotic form of the Franz-Keldysh shape: $\mathrm{exp}(\ensuremath{-}\frac{{{C}_{0}}^{\ensuremath{'}}{|E\ensuremath{-}{{E}_{0}}^{\ensuremath{'}}|}^{\frac{3}{2}}}{f})$. Physical arguments are presented to show why the exciton effects should be important. A discussion is presented of the interrelationships among the present treatment of electro-absorption and various one-electron, exciton, and many-body formalisms.

••

TL;DR: In this article, the electronic band structure of graphite has been calculated from an ab initio variational approach using a linear-combination of atomic-orbitals (LCAO) basis of Bloch states, including nonspherical terms in the one-electron crystal potential.

Abstract: The electronic band structure of graphite has been calculated from an ab initio variational approach using a linear-combination of atomic-orbitals (LCAO) basis of Bloch states, including nonspherical terms in the one-electron crystal potential. Matrix elements of the Hamiltonian are evaluated directly without any tight-binding approximations. The optical transitions deduced from the energy bands calculated using a single-layer crystal model agree nicely with recent polarized-light reflectance measurements. Details of the band structure are calculated for the three-dimensional Brillouin zone and related to the results obtained using the single-layer crystal structure. The results are encouraging, not only from the standpoint that the method employed is an ab initio approach with no special a priori assumptions, but also because the band structure is quite insensitive to the particulars of the crystal potential function.

••

TL;DR: In this article, a theory of photoemission is presented in which all results are derived rigorously from first principles, and it is shown how to calculate properly the external current of electrons, with the transmission at the surface done correctly.

Abstract: A theory of photoemission is presented in which all results are derived rigorously from first principles. It is shown how to calculate properly the external current of electrons, with the transmission at the surface done correctly. A new and rigorous formalism is derived for doing many-body calculations in photoemission. Extensive calculations are performed on the angular dependence of photoemission. It is shown that the angular anisotropy is interesting and significant. Numerous numerical examples are presented for the alkali metals.

••

TL;DR: In this article, a general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed, besides the well-known Ising and "ice" models, other soluble cases are also considered.

Abstract: A general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed. Besides the well-known Ising and "ice" models, other soluble cases are also considered. After discussing some general symmetry properties of this model, we consider in detail a particular class of the soluble cases, the "free-fermion" model. The explicit expressions for all thermodynamic functions with the inclusion of an external electric field are obtained. It is shown that both the specific heat and the polarizability of the free-fermion model exhibit in general a logarithmic singularity. An inverse-square-root singularity results, however, if the free-fermion model also satisfies the ice condition. The results are illustrated with a specific example.

••

TL;DR: In this article, a simple empirical relation is found between the linear and the third-order nonlinear optical susceptibilities for gases at low pressures, and its applicability to crystalline solids and its bearing on the generalized Miller's rule for these solids is discussed.

Abstract: A simple empirical relation is found to exist between the linear and the third-order nonlinear optical susceptibilities This empirical relation holds within the available experimental accuracy for gases at low pressures The applicability of this empirical relation to crystalline solids, and its bearing on the generalized Miller's rule for these solids, are discussed

••

TL;DR: In this paper, the real and imaginary parts of the dielectric constant of Au were accurately determined in the 0.5-6-eV range from measurements of the reflectance and transmittance of thin semitransparent films.

Abstract: Both the real and imaginary parts of the dielectric constant of Au were accurately determined in the 0.5-6-eV range from measurements of the reflectance and transmittance of thin semitransparent films. The results obtained on well-crystallized films were in general agreement with previous data on bulk samples. They allowed a thorough analysis of the absorption spectrum of Au in terms of intra- and interband transitions. Deviations from the Drude theory were observed, and the values of the optical mass and relaxation time of the conduction electrons are discussed. The absorption edge was investigated very accurately. Further information on the absorption processes was also obtained by studying films with different crystallographic structures. In particular, the supplementary absorption often observed in Au below the absorption edge was shown to be due to impurities.