Low-Energy Effective Hamiltonian and the Surface States of Ca_3PbO

The band structure of Ca_3PbO, which possesses a three-dimensional massive Dirac electron at the Fermi energy, is investigated in detail. Analysis of the orbital weight distributions on the bands obtained in the first-principles calculation reveals that the bands crossing the Fermi energy originate from the three Pb-p orbitals and three Ca-dx2y2 orbitals. Taking these Pb-p and Ca-dx2y2 orbitals as basis wave functions, a tight-binding model is constructed. With the appropriate choice of the hopping integrals and the strength of the spin-orbit coupling, the constructed model sucessfully captures important features of the band structure around the Fermi energy obtained in the first-principles calculation. By applying the suitable basis transformation and expanding the matrix elements in the series of the momentum measured from a Dirac point, the low-energy effective Hamiltonian of this model is explicitely derived and proved to be a Dirac Hamiltonain. The origin of the mass term is also discussed. It is shown that the spin-orbit coupling and the orbitals other than Pb-p and Ca-dx2y2 orbitals play important roles in making the mass term finite. Finally, the surface band structures of Ca_3PbO for several types of surfaces are investigated using the constructed tight-binding model. We find that there appear nontrivial surface states that cannot be explained as the bulk bands projected on the surface Brillouin zone. The relation to the topological insulator is also discussed.Comment: 11 page

Direct bandgap silicon through strain engineering of type-VIII silicon clathrate Si46: A first-principles study

2-s2.0-85083164243In this work, we suggest a way to achieve a direct bandgap silicon clathrate by means of first-principles calculations. Effects of biaxial-strain on physical properties of type-VIII silicon clathrate Si46 are investigated. For that purpose, biaxial strain tensors (?4%<? <+6%) have been exerted along the <100> and <010> in-plane directions, while the out-of-plane <001> axis is strain-free. Under normal conditions, type-VIII Si46 is indirect bandgap semiconductor with magnitude of about 1.152eV (GGA-PBE). For sake of comparison, the band structure was as well calculated by means of the hybrid PBE0 functional, in that case its allure and nature were not affected, whereas the bandgap's magnitude was increased to 2.62eV (Hybrid PBE0). It was observed that a tensile strain of +4% and above will induce a bandgap alteration from indirect to direct where both the conduction band minimum CBM and the valence band maximum VBM are located at the same point within the ?(0,0,0)–H(1/2,1/2,-1/2) symmetry segment (?). Optical properties revealed better spectrums for the +4% strained material with direct bandgap as the optical light absorption was increased by about 12%. These findings play in favor for this material as a candidate for future “all-Si” photonic and photovoltaic devices. © 2020 Elsevier B.V

Fabella prevalence rate increases over 150 years, and rates of other sesamoid bones remain constant: a systematic review

The fabella is a sesamoid bone located behind the lateral femoral condyle. It is common in non-human mammals, but the prevalence rates in humans vary from 3 to 87%. Here, we calculate the prevalence of the fabella in a Korean population and investigate possible temporal shifts in prevalence rate. A total of 52.83% of our individuals and 44.34% of our knees had fabellae detectable by computed tomography scanning. Men and women were equally likely to have a fabella, and bilateral cases (67.86%) were more common than unilateral ones (32.14%). Fabella presence was not correlated with height or age, although our sample did not include skeletally immature individuals. Our systematic review yielded 58 studies on fabella prevalence rate from 1875-2018 which met our inclusion criteria, one of which was an outlier. Intriguingly, a Bayesian mixed effects generalized linear model revealed a temporal shift in prevalence rates, with the median prevalence rate in 2000 (31.00%) being ~ 3.5 times higher than that in 1900 (7.64%). In all four countries with studies before and after 1960, higher rates were always found after 1960. Using data from two other systematic reviews, we found no increase in prevalence rates of 10 other sesamoid bones in the human body, indicating that the increase in fabella prevalence rate is unique. Fabella presence/absence is due to a combination of genetic and environmental factors: as the prevalence rates of other sesamoid bones have not changed in the last 100 years, we postulate the increase in fabella prevalence rate is due to an environmental factor. Namely, the global increase in human height and weight (due to improved nutrition) may have increased human tibial length and muscle mass. Increases in tibial length could lead to a larger moment arm acting on the knee and on the tendons crossing it. Coupled with the increased force from a larger gastrocnemius, this could produce the mechanical stimuli necessary to initiate fabella formation and/or ossification