Electronic Structure of the Chevrel-Phase Compounds Snx_{x}Mo6_{6}Se7.5_{7.5}: Photoemission Spectroscopy and Band-structure Calculations

We have studied the electronic structure of two Chevrel-phase compounds, Mo$_6$Se$_{7.5}$ and Sn$_{1.2}$Mo$_6$Se$_{7.5}$, by combining photoemission spectroscopy and band-structure calculations. Core-level spectra taken with x-ray photoemission spectroscopy show systematic core-level shifts, which do not obey a simple rigid-band model. The inverse photoemission spectra imply the existence of an energy gap located $\sim 1$ eV above the Fermi level, which is a characteristic feature of the electronic structure of the Chevrel compounds. Quantitative comparison between the photoemission spectra and the band-structure calculations have been made. While good agreement between theory and experiment in the wide energy range was obtained as already reported in previous studies, we found that the high density of states near the Fermi level predicted theoretically due to the Van Hove singularity is considerably reduced in the experimental spectra taken with higher energy resolution than in the previous reports. Possible origins are proposed to explain this observation.Comment: 8 pages, 5 figure

Insights from ARPES for an undoped, four-layered, two-gap high-T_c superconductor

An undoped cuprate with apical fluorine and inner (i) and outer (o) CuO2-layers is a 60 K superconductor whose Fermi surface (FS) has large n- and p-doped sheets with the SC gap on the n-sheet twice that on the p -sheet (Y. Chen et al.). The Fermi surface is not reproduced by the LDA, but the screening must be substantially reduced due to electronic correlations, and oxygen in the o-layers must be allowed to dimple outwards. This charges the i-layers by 0.01|e|, causes an 0.4 eV Madelung-potential difference between the i and o -layers, quenches the i-o hopping, and localizes the n-sheets onto the i-layers, thus protecting their d-wave pairs from being broken by scattering on impurities in the BaF layers. The correlation-reduced screening strengthens the coupling to z-axis phonons.Comment: 4 pages, 3 figure

Superconductivity in Boron under pressure - why are the measured Tc_c's so low?

Using the full potential linear muffin-tin orbitals (FP-LMTO) method we examine the pressure-dependence of superconductivity in the two metallic phases of Boron: bct and fcc. Linear response calculations are carried out to examine the phonon frequencies and electron-phonon coupling for various lattice parameters, and superconducting transition temperatures are obtained from the Eliashberg equation. In both bct and fcc phases the superconducting transition temperature T$_c$ is found to decrease with increasing pressure, due to stiffening of phonons with an accompanying decrease in electron-phonon coupling. This is in contrast to a recent report, where T$_c$ is found to increase with pressure. Even more drastic is the difference between the measured T$_c$, in the range 4-11 K, and the calculated values for both bct and fcc phases, in the range 60-100 K. The calculation reveals that the transition from the fcc to bct phase, as a result of increasing volume or decreasing pressure, is caused by the softening of the X-point transverse phonons. This phonon softening also causes large electron-phonon coupling for high volumes in the fcc phase, resulting in coupling constants in excess of 2.5 and T$_c$ nearing 100 K. We discuss possible causes as to why the experiment might have revealed T$_c$'s much lower than what is suggested by the present study. The main assertion of this paper is that the possibility of high T$_c$, in excess of 50 K, in high pressure pure metallic phases of boron cannot be ruled out, thus substantiating the need for further experimental investigations of the superconducting properties of high pressure pure phases of boron.Comment: 16 pages, 8 figures, 1 Tabl

Calculations of Hubbard U from first-principles

The Hubbard \emph{U} of the \emph{3d} transition metal series as well as SrVO$_{3}$, YTiO$_{3}$, Ce and Gd has been estimated using a recently proposed scheme based on the random-phase approximation. The values obtained are generally in good accord with the values often used in model calculations but for some cases the estimated values are somewhat smaller than those used in the literature. We have also calculated the frequency-dependent \emph{U} for some of the materials. The strong frequency dependence of \emph{U} in some of the cases considered in this paper suggests that the static value of \emph{U} may not be the most appropriate one to use in model calculations. We have also made comparison with the constrained LDA method and found some discrepancies in a number of cases. We emphasize that our scheme and the constrained LDA method theoretically ought to give similar results and the discrepancies may be attributed to technical difficulties in performing calculations based on currently implemented constrained LDA schemes.Comment: 24 pages, 13 figures; Submitted to Phys. Rev.

Developing the MTO Formalism

We review the simple linear muffin-tin orbital method in the atomic-spheres approximation and a tight-binding representation (TB-LMTO-ASA method), and show how it can be generalized to an accurate and robust Nth order muffin-tin orbital (NMTO) method without increasing the size of the basis set and without complicating the formalism. On the contrary, downfolding is now more efficient and the formalism is simpler and closer to that of screened multiple-scattering theory. The NMTO method allows one to solve the single-electron Schroedinger equation for a MT-potential -in which the MT-wells may overlap- using basis sets which are arbitrarily minimal. The substantial increase in accuracy over the LMTO-ASA method is achieved by substitution of the energy-dependent partial waves by so-called kinked partial waves, which have tails attached to them, and by using these kinked partial waves at N+1 arbitrary energies to construct the set of NMTOs. For N=1 and the two energies chosen infinitesimally close, the NMTOs are simply the 3rd-generation LMTOs. Increasing N, widens the energy window, inside which accurate results are obtained, and increases the range of the orbitals, but it does not increase the size of the basis set and therefore does not change the number of bands obtained. The price for reducing the size of the basis set through downfolding, is a reduction in the number of bands accounted for and -unless N is increased- a narrowing of the energy window inside which these bands are accurate. A method for obtaining orthonormal NMTO sets is given and several applications are presented.Comment: 85 pages, Latex2e, Springer style, to be published in: Lecture notes in Physics, edited by H. Dreysse, (Springer Verlag

Taking a Knee: Effect of NFL Player Protests on Subsequent Employment and Earnings

Protesters sometimes face penalties for their actions, but few papers have attempted to quantify these penalties. We investigate whether the subsequent salaries and employment status of NFL players who took a knee or sat during the national anthem during the 2017 season differed from similar players who did not. We find limited evidence that they were penalized in terms of employment during the 2018 or 2019 seasons. Conditional on employment, we find an insignificant relationship between protesting and log salaries