Three-dimensional (3D) Dirac point, where two Weyl points overlap in momentum space, is usually unstable and hard to realize. Here we show, based on the first-principles calculations and effective model analysis, that crystalline A3Bi (A=Na, K, Rb) are Dirac semimetals with bulk 3D Dirac points protected by crystal symmetry. They possess nontrivial Fermi arcs on the surfaces and can be driven into various topologically distinct phases by explicit breaking of symmetries. Giant diamagnetism, linear quantum magnetoresistance, and quantum spin Hall effect will be expected for such compounds.

We investigate the behavior of holes in the valence band of a range of wide-band-gap oxides including ZnO, MgO, In2O3, Ga2O3, Al2O3, SnO2, SiO2, and TiO2. Based on hybrid functional calculations, we find that, due to the orbital composition of the valence band, holes tend to form localized small polarons with characteristic lattice distortions, even in the absence of defects or impurities. These self-trapped holes (STHs) are energetically more favorable than delocalized, free holes in the valence band in all materials but ZnO and SiO2. Based on calculated optical absorption and emission energies we show that STHs provide an explanation for the luminescence peaks that have been observed in many of these oxides. We demonstrate that polaron formation prohibits p-type conductivity in this class of materials.

Employing the random phase approximation we investigate the binding energy and Van der Waals (vdW) interlayer spacing between the two layers of bilayer transition metal dichalcogenides ${\mathrm{MoS}}_{2}$, ${\mathrm{MoSe}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$ for five different stacking patterns, and examine the stacking-induced modifications on the electronic and optical/excitonic properties within the GW approximation with a priori inclusion of spin-orbit coupling and by solving the two-particle Bethe-Salpeter equation. Our results show that for all cases, the most stable stacking order is the high symmetry $A{A}^{$'${}}$ type, distinctive of the bulklike $2H$ symmetry, followed by the $AB$ stacking fault, typical of the $3R$ polytypism, which is by only 5 meV/formula unit less stable. The conduction band minimum is always located in the midpoint between K and $$\Gamma${}$, regardless of the stacking and chemical composition. All $M{X}_{2}$ undergo an direct-to-indirect optical gap transition going from the monolayer to the bilayer regime. The stacking and the characteristic vdW interlayer distance mainly influence the valence band splitting at K and its relative energy with respect to $$\Gamma${}$, as well as, the electron-hole binding energy and the values of the optical excitations.

A combination of scanning tunneling microscopy and spectroscopy and density functional theory is used to characterize excess electrons in ${\mathrm{TiO}}_2$ rutile and anatase, two prototypical materials with identical chemical composition but different crystal lattices. In rutile, excess electrons can localize at any lattice Ti atom, forming a small polaron, which can easily hop to neighboring sites. In contrast, electrons in anatase prefer a free-carrier state, and can only be trapped near oxygen vacancies or form shallow donor states bound to Nb dopants. The present study conclusively explains the differences between the two polymorphs and indicates that even small structural variations in the crystal lattice can lead to a very different behavior.

The development of high efficiency perovskite solar cells has sparked a multitude of measurements on the optical properties of these materials. For the most studied methylammonium(MA)PbI₃ perovskite, a large range (6–55 meV) of exciton binding energies has been reported by various experiments. The existence of excitons at room temperature is unclear. For the MAPbX₃ perovskites we report on relativistic Bethe-Salpeter Equation calculations (GW-BSE). This method is capable to directly calculate excitonic properties from first-principles. At low temperatures it predicts exciton binding energies in agreement with the reported ‘large’ values. For MAPbI₃, phonon modes present in this frequency range have a negligible contribution to the ionic screening. By calculating the polarization in time from finite temperature molecular dynamics, we show that at room temperature this does not change. We therefore exclude ionic screening as an explanation for the experimentally observed reduction of the exciton binding energy at room temperature and argue in favor of the formation of polarons.