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Register a new userRole of the exchange-correlation functional on the structural, electronic and optical properties of cubic and tetragonal SrTiO$_3$ including many-body effects
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SrTiO$_3$ is a model perovskite compound with unique properties and technological relevance. At 105 K it undergoes a transition from a cubic to a tetragonal phase with characteristic antiferrodistortive rotations of the TiO$_6$ octahedra. Here we study systematically the effect of different exchange correlation functionals on the structural, electronic and optical properties of cubic and tetragonal STO by comparing the recently implemented strongly constrained and appropriately normed (SCAN) meta-GGA functional with the generalized gradient approximation (PBE96 and PBEsol) and the hybrid functional (HSE06). SCAN is found to significantly improve the description of the structural properties, in particular the rotational angle of the tetragonal phase, comparable to HSE06 at a computational cost similar to GGA. The addition of a Hubbard $U$-term (SCAN+$U$, $U=7.45$ eV) allows to achieve the experimental band gap of 3.25 eV with a moderate increase in the lattice constant, whereas within GGA+$U$ the gap is underestimated even for high $U$ values. The effect of the exchange-correlation functional on the optical properties is progressively reduced from 1.5 eV variance in the onset of the spectrum in the independent particle picture to 0.3 eV upon inclusion of many-body effects within the framework of the $GW$ approximation (single-shot $G_0W_0$) and excitonic corrections by solving the Bethe-Salpeter equation (BSE). Moreover, a model BSE approach is shown to reproduce the main features of the optical spectrum at a lower cost compared to $G_0W_0$+BSE. Strong excitonic effects are found in agreement with previous results and their origin is analyzed based on the contributing interband transitions. Last but not least, the effect of the tetragonal distortion on the optical spectrum is discussed and compared to available experimental data.
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Here we report the optical and x-ray absorption (XAS) spectra of the wide-band-gap oxide MgO using density functional theory (DFT) and many-body perturbation theory (MBPT). Our comprehensive study of the electronic structure shows that while the band gap is underestimated with the exchange-correlation functional PBEsol (4.58 eV) and the hybrid functional HSE06 (6.58 eV) compared to the experimental value (7.7 eV), it is significantly improved (7.52 eV) and even overcompensated (8.53 eV) when quasiparticle corrections are considered. Inclusion of excitonic effects by solving the Bethe-Salpeter equation (BSE) yields the optical spectrum in excellent agreement with experiment. Excellent agreement is observed also for the O and Mg K-edge absorption spectra, demonstrating the importance of the electron-hole interaction within MBPT. Projection of the electron-hole coupling coefficients from the BSE eigenvectors on the band structure allows us to determine the origin of prominent peaks and identify the orbital character of the relevant contributions. The real space projection of the lowest energy exciton wavefunction of the optical spectrum indicates a Wannier-Mott type, whereas the first exciton in the O K-edge is more localized.
We present many-body textit{ab initio} calculations of the electronic and optical properties of semiconducting zigzag carbon nanotubes under uniaxial strain. The GW approach is utilized to obtain the quasiparticle bandgaps and is combined with the Bethe-Salpeter equation to obtain the optical absorption spectrum. We find that the dependence of the electronic bandgaps on strain is more complex than previously predicted based on tight-binding models or density-functional theory. In addition, we show that the exciton energy and exciton binding energy depend significantly on strain, with variations of tens of meVs per percent strain, but that despite these strong changes the absorbance is found to be nearly independent of strain. Our results provide new guidance for the understanding and design of optomechanical systems based on carbon nanotubes.
We report the effect of oxygen pressure during growth ($P_{O_{2}}$) on the electronic and magnetic properties of PrAlO$_3$ films grown on $rm TiO_{2}$-terminated SrTiO$_3$ substrates. Resistivity measurements show an increase in the sheet resistance as $P_{O_{2}}$ is increased. The temperature dependence of the sheet resistance at low temperatures is consistent with Kondo theory for $P_{O_{2}} ge 10^{-5}$ torr. Hall effect data exhibit a complex temperature dependence that suggests a compensated carrier density. We observe behavior consistent with two different types of carriers at interfaces grown at $P_{O_{2}} ge 10^{-4}$ torr. For these interfaces, we measured a moderate positive magnetoresistance (MR) due to a strong spin-orbit (SO) interaction at low magnetic fields that evolves into a larger negative MR at high fields. Positive high MR values are associated with samples where a fraction of carriers are derived from oxygen vacancies. Analysis of the MR data permitted the extraction of the SO interaction critical field ( e.g. $ H_{SO}=$1.25 T for $P_{O_{2}}=10^{-5}$ torr). The weak anti-localization effect due to a strong SO interaction becomes smaller for higher $P_{O_{2}}$ grown samples, where MR values are dominated by the Kondo effect, particularly at high magnetic fields.
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 prototypical 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.
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