Structural, electronic, vibrational and dielectric properties of LaBGeO$_5$ with the stillwellite structure are determined based on textit{ab initio} density functional theory. The theoretically relaxed structure is found to agree well with the exist
ing experimental data with a deviation of less than $0.2%$. Both the density of states and the electronic band structure are calculated, showing five distinct groups of valence bands. Furthermore, the Born effective charge, the dielectric permittivity tensors, and the vibrational frequencies at the center of the Brillouin zone are all obtained. Compared to existing model calculations, the vibrational frequencies are found in much better agreement with the published experimental infrared and Raman data, with absolute and relative rms values of 6.04 cm$^{-1}$, and $1.81%$, respectively. Consequently, numerical values for both the parallel and perpendicular components of the permittivity tensor are established as 3.55 and 3.71 (10.34 and 12.28), respectively, for the high-(low-)frequency limit.
We extend recent textit{ab initio} calculations of the electronic band structure and the phonon dispersion relations of rhombohedral GeTe to calculations of the density of phonon states and the temperature dependent specific heat. The results are com
pared with measurements of the specific heat. It is discovered that the specific heat depends on hole concentration, not only in the very low temperature region (Sommerfeld term) but also at the maximum of $C_p/T^3$ (around 16 K). To explain this phenomenon, we have performed textit{ab initio} lattice dynamical calculations for GeTe rendered metallic through the presence of a heavy hole concentration ($p$ $sim$ 2$times$ 10$^{21}$ cm$^{-3}$). They account for the increase observed in the maximum of $C_p/T^3$.
Using a linear combination of atomic orbitals approach, we report a systematic comparison of various Density Functional Theory (DFT) and hybrid exchange-correlation functionals for the prediction of the electronic and structural properties of prototy
pical ferroelectric oxides. It is found that none of the available functionals is able to provide, at the same time, accurate electronic and structural properties of the cubic and tetragonal phases of BaTiO$_3$ and PbTiO$_3$. Some, although not all, usual DFT functionals predict the structure with acceptable accuracy, but always underestimate the electronic band gaps. Conversely, common hybrid functionals yield an improved description of the band gaps, but overestimate the volume and atomic distortions associated to ferroelectricity, giving rise to an unacceptably large $c/a$ ratio for the tetragonal phases of both compounds. This super-tetragonality is found to be induced mainly by the exchange energy corresponding to the Generalized Gradient Approximation (GGA) and, to a lesser extent, by the exact exchange term of the hybrid functional. We thus propose an alternative functional that mixes exact exchange with the recently proposed GGA of Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] which, for solids, improves over the treatment of exchange of the most usual GGAs. The new functional renders an accurate description of both the structural and electronic properties of typical ferroelectric oxides.
The dynamical, dielectric and elastic properties of GeTe, a ferroelectric material in its low temperature rhombohedral phase, have been investigated using first-principles density functional theory. We report the electronic energy bands, phonon dispe
rsion curves, electronic and low frequency dielectric tensors, infra-red reflectivity, Born effective charges, elastic and piezoelectric tensors and compare them with the existing theoretical and experimental results, as well as with similar quantities available for other ferroelectric materials, when appropriate.
We use many-body perturbation theory, the state-of-the-art method for band gap calculations, to compute the band offsets at the Si/SiO$_2$ interface. We examine the adequacy of the usual approximations in this context. We show that (i) the separate t
reatment of band-structure and potential lineup contributions, the latter being evaluated within density-functional theory, is justified, (ii) most plasmon-pole models lead to inaccuracies in the absolute quasiparticle corrections, (iii) vertex corrections can be neglected, (iv) eigenenergy self-consistency is adequate. Our theoretical offsets agree with the experimental ones within 0.3 eV.
