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Hexagonal SiGe is a promising material for combining electronic and photonic technologies. In this work, the energetic, structural, elastic and electronic properties of the hexagonal polytypes (2$H$, 4$H$ and 6$H$) of silicon and germanium are thoroughly analyzed under equilibrium conditions. For this purpose, we apply state-of-the-art density functional theory. The phase diagram, obtained in the framework of a generalized Ising model, shows that the diamond structure is the most stable under ambient conditions, but hexagonal modifications are close to the phase boundary, especially for Si. Our band-structure calculations using the MBJLDA and HSE06 exchange correlation functionals predict significant changes in electronic states with hexagonality. While Si crystals are always semiconductors with indirect band gaps, the hexagonal Ge polytypes have direct band gaps. The branch point energies for Ge crystals are below the valence band maxima, and therefore the formation of hole gases on Ge surfaces is favoured. Band alignment based on the branch point energy leads to type-I heterocrystalline interfaces between Ge polytypes, where electrons and holes can be trapped in the layer with the higher hexagonality. In contrast, the energy shift of the indirect conduction band minima of Si polytypes is rather weak, leading to delocalization of excited electrons at interfaces, while only holes can localize in the layer with higher hexagonality., Comment: 37 pages, 7 figures, submitted to Physical Review Materials

We present ab initio calculations of the electronic and optical properties of hexagonal SiGe alloys in the lonsdaleite structure. Lattice constants and electronic band structures in excellent agreement with experiment are obtained using density-functional theory. Hexagonal Si has an indirect band gap, while hexagonal Ge has a pseudo-direct gap, i.e. the optical transitions at the minimum direct band gap are very weak. The pseudo-direct character of pure hexagonal Ge is efficiently lifted by alloying. Already for a small admixture of Si, symmetry reduction enhances the oscillator strength of the lowest direct optical transitions. The band gap is direct for a Si content below 45 %. We validate lonsdaleite group-IV alloys to be efficient optical emitters, suitable for integrated optoelectronic applications.

Lonsdaleite germanium has a direct band gap, but it is not an efficient light emitter due to the vanishing oscillator strength of electronic transitions at the fundamental gap. Transitions involving the second lowest conduction band are instead at least three orders of magnitude stronger. The inversion of the two lowest conduction bands would therefore make hexagonal germanium ideal for optoelectronic applications. In this work, we investigate the possibility to achieve this band inversion by applying strain. To this end we perform ab initio calculations of the electronic band structure and optical properties of strained hexagonal germanium, using density functional theory with the modified Becke-Johnson exchange-correlation functional and including spin-orbit interaction. We consider hydrostatic pressure, uniaxial strain along the hexagonal c axis, as well as biaxial strain in planes perpendicular to and containing the hexagonal c axis to simulate the effect of a substrate. We find that the conduction-band inversion, and therefore the transition from a pseudo-direct to a direct band gap, is attainable for moderate tensile uniaxial strain parallel to the lonsdaleite c axis.

The search for new wide band gap materials is intensifying to satisfy the need for more advanced and energy efficient power electronic devices. Ga$_2$O$_3$ has emerged as an alternative to SiC and GaN, sparking a renewed interest in its fundamental properties beyond the main $\beta$-phase. Here, three polymorphs of Ga$_2$O$_3$, $\alpha$, $\beta$ and $\varepsilon$, are investigated using X-ray diffraction, X-ray photoelectron and absorption spectroscopy, and ab initio theoretical approaches to gain insights into their structure - electronic structure relationships. Valence and conduction electronic structure as well as semi-core and core states are probed, providing a complete picture of the influence of local coordination environments on the electronic structure. State-of-the-art electronic structure theory, including all-electron density functional theory and many-body perturbation theory, provide detailed understanding of the spectroscopic results. The calculated spectra provide very accurate descriptions of all experimental spectra and additionally illuminate the origin of observed spectral features. This work provides a strong basis for the exploration of the Ga$_2$O$_3$ polymorphs as materials at the heart of future electronic device generations., Comment: Updated manuscript version after peer review

The third-rank tensor of the static spin Hall conductivity is investigated for two-dimensional (2D) topological insulators by electronic structure calculations. Its seeming quantization is numerically demonstrated for highly symmetric systems independent of the gap size. 2D crystals with hexagonal and square Bravais lattice show similar effects, while true rectangular translational symmetry yields conductivity values much below the quantum $e^2/h$. Field-induced lifting the inversion symmetry does not influence the quantum spin Hall state up to band inversion but the conductivity quantization. Weak symmetry-conserving biaxial but also uniaxial strain has a minor influence as long as inverted gaps dictate the topological character. The results are discussed in terms of the atomic geometry and the Rashba contribution to the spin-orbit interaction (SOI). Translational and point-group symmetry as well as SOI rule the deviation from the quantization of the spin Hall conductance.

High-quality defect-free lonsdaleite Si and Ge can now be grown on hexagonal nanowire substrates. These hexagonal phases of group-IV semiconductors have been predicted to exhibit improved electronic and optical properties for optoelectronic applications. While lonsdaleite Si is a well-characterized indirect semiconductor, experimental data and reliable calculations on lonsdaleite Ge are scarce and not consistent regarding the nature of its gap. Using ab initio density-functional theory, we calculate accurate structural, electronic, and optical properties for hexagonal Ge. Given the well-known sensitivity of electronic-structure calculations for Ge to the underlying approximations, we systematically test the performance of several exchange-correlation functionals, including meta-GGA and hybrid functionals. We first validate our approach for cubic Ge, obtaining atomic geometries and band structures in excellent agreement with available experimental data. Then, the same approach is applied to predict electronic and optical properties of lonsdaleite Ge. We portray lonsdaleite Ge as a direct semiconductor with only weakly dipole-active lowest optical transitions, small band gap, huge crystal-field splitting, and strongly anisotropic effective masses. The unexpectedly small direct gap and the oscillator strengths of the lowest optical transitions are explained in terms of symmetry and back-folding of energy bands of the diamond structure.

We apply a generalized model for the determination and analysis of the dielectric function of optically anisotropic materials with colour dispersion to phonon modes and show that it can also be generalized to excitonic polarizabilities and electronic band-band transitions. We take into account that the tensor components of the dielectric function within the cartesian coordinate system are not independent from each other but are rather projections of the polarization of dipoles oscillating along directions defined by the, non-cartesian, crystal symmetry and polarizability. The dielectric function is then composed of a series of oscillators pointing in different directions. The application of this model is exemplarily demonstrated for monoclinic ($\beta$-phase) Ga$_2$O$_3$ bulk single crystals. Using this model, we are able to relate electronic transitions observed in the dielectric function to atomic bond directions and orbitals in the real space crystal structure. For thin films revealing rotational domains we show that the optical biaxiality is reduced to uniaxial optical response., Comment: 10 pages, 6 figures

The dielectric tensor of $\beta$-Ga$_2$O$_3$ was determined by generalized spectroscopic ellipsometry in a wide spectral range from $0.5\,\mathrm{eV}$ to $8.5\,\mathrm{eV}$ as well as by calculation including quasiparticle bands and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to $|\varepsilon_{xz} | \approx 0.30 $ and cannot be neglected. Even in the transparent spectral range where it is quite small ($|\varepsilon_{xz} | < 0.02 $) it causes a rotation of the dielectric axes around the symmetry axis of up to $20^\circ$.

Electronic excitations and optical spectra of $CdF_{2}$ are calculated up to ultraviolet employing state-of-the-art techniques based on density functional theory and many-body perturbation theory. The GW scheme proposed by Hedin has been used for the electronic self-energy to calculate single-particle excitation properties as energy bands and densities of states. For optical properties many-body effects, treated within the Bethe-Salpeter equation framework, turn out to be crucial. A bound exciton located about 1 eV below the quasiparticle gap is predicted. Within the present scheme the optical absorption spectra and other optical functions show an excellent agreement with experimental data. Moreover, we tested different schemes to obtain the best agreement with experimental data. Among the several schemes, we suggest a self-consistent quasiparticle energy scheme., Comment: Accepted on PRB

The quasiparticle band structures of four polytypes 3C, 6H, 4H, and 2H of GaP, GaAs, GaSb, InP, InAs, and InSb are computed with high accuracy including spin-orbit interaction applying a recently developed approximate calculation scheme, the LDA-1/2 method. The results are used to derive band offsets $\Delta E_c$ and $\Delta E_v$ for the conduction and valence bands between two polytypes. The alignment of the band structures is based on the branch-point energy $E_{\rm BP}$ for each polytype. The aligned electronic structures are used to explain properties of heterocrystalline but homomaterial junctions. The gaps and offsets allow to discuss spectroscopic results obtained recently for such junctions in III-V nanowires.