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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

Using a variational approach, the binding energies $E_b$ of the lowest bound excitons in Xenes under varying electric field are investigated. The internal exciton motion is described both by Dirac electron dispersion and in effective-mass approximation, while the screened electron-hole attraction is modeled by a Rytova-Keldysh potential with a 2D electronic polarizability $\alpha_{2{\rm D}}$. The most important parameters as spin-orbit-induced gap $E_g$, Fermi velocity $v_F$ and $\alpha_{2{\rm D}}$ are taken from ab initio density functional theory calculations. In addition, $\alpha_{2{\rm D}}$ is approximated in two different ways. The relation of $E_b$ and $E_g$ is ruled by the screening. The existence of an excitonic insulator phase with $E_b>E_g$ sensitively depends on the chosen $\alpha_{2{\rm D}}$. The values of $E_g$ and $\alpha_{2{\rm D}}$ are strongly modified by a vertical external electric bias $U$, which defines a transition from the topological into a trivial insulator at $U=E_g/2$, with the exception of plumbene. Within the Dirac approximation, but also within the effective mass description of the kinetic energy, the treatment of screening dominates the appearance or non-appearance of an excitonic insulator phase. Gating does not change the results: the prediction done at zero electric field is confirmed when a vertical electric field is applied. Finally, Many-Body perturbation theory approaches based on the Green's function method, applied to stanene, confirm the absence of an excitonic insulator phase, thus validating our results obtained by ab initio modeling of $\alpha_{2{\rm D}}$.

We present a comprehensive first-principles investigation of optical, transport, and thermoelectric properties of pure and doped hexagonal Si$_x$Ge$_{1-x}$ alloys based on density-functional theory calculations, the Boltzmann transport equation, and the generalized quasi-chemical approximation to obtain alloy averages of electronic properties. At low temperature, phase decomposition into the hexagonal elementary crystals is thermodynamically favored, but around and above room temperature random alloys are predicted to be stable. While hexagonal Si has an indirect band gap, the gap of hexagonal Ge is direct with very weak optical transitions at the absorption edge. The alloy band gap remains direct for a Si content below 45\,\% and the oscillator strength of the lowest optical transitions is efficiently enhanced by alloying. The optical spectra show clear trends and both absorption edges and prominent peaks can be tuned with composition. The dependence of transport coefficients on carrier concentration and temperature is similar in cubic and hexagonal alloys. However, the latter display anisotropic response due to the reduced hexagonal symmetry. In particular, the transport mass exhibits a significant directional dependence. Seebeck coefficients and thermoelectric power factors of $n$-doped alloys show non-monotonous variations with the Si content independently of temperature.

The natural and true band profiles at heterojunctions formed by hexagonal Si$_x$Ge$_{1-x}$ alloys are investigated by a variety of methods: density functional theory for atomic geometries, approximate quasiparticle treatments for electronic structures, different band edge alignment procedures, and construction of various hexagonal unit cells to model alloys and heterojunctions. We demonstrate that the natural band offsets are rather unaffected by the choice to align the vacuum level or the branch point energy, as well as by the use of a hybrid or the Tran-Blaha functional. At interfaces between Ge-rich alloys we observe a type-I heterocharacter with direct band gaps, while Si-rich junctions are type-I but with an indirect band gap. The true band lineups at pseudomorphically grown heterostructures are strongly influenced by the generated biaxial strain of opposite sign in the two adjacent alloys. Our calculations show that the type-I character of the interface is reduced by strain. To prepare alloy heterojunctions suitable for active optoelectronic applications, we discuss how to decrease the compressive biaxial strain at Ge-rich alloys., Comment: 23 pages, 8 figures

We present ab initio calculations of electronic and optical properties of perturbed hexagonal germanium and demonstrate that it is a superior material for active optoelectronic devices in the infrared spectral region. It is known that perfect lonsdaleite Ge is a pseudodirect semiconductor, i.e., with direct fundamental band gap but almost vanishing oscillator strength for the lowest-energy optical transitions. Perturbing the system by replacing a Ge atom in the unit cell with a Si atom boosts of the oscillator strength at the minimum direct gap by orders of magnitude, with a concurrent blue shift of the interband distances. This effect is mainly due to the increased s character of the lowest conduction band because of the perturbation-induced wave function mixing. A purely structural modification of the lonsdaleite unit cell of hexagonal Ge yields as well increased optical oscillator strengths, but their magnitude significantly depends on the actual details of the atomic geometry. In particular, moderate tensile uniaxial strain can induce an inversion of the order of the two lowest conduction bands, immediately leading to an extremely efficient enhancement of optical transitions. In general, chemical and/or structural perturbations of the lonsdaleite lattice are shown to be the key to make hexagonal germanium suitable for light emitting devices.

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 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.

By means of $ab \ initio$ band structure methods and model Hamiltonians we investigate the electronic, spin and topological properties of four monopnictides crystallizing in body centered tetragonal structure. We show that the Weyl bands around a Weyl point W1 or W2 possess a strong anisotropy and tilt of the accompanying Dirac cones. These effects are larger for W2 nodes than for W1 ones. The node tilts and positions in energy space significantly influence the density of states of single-particle Weyl excitations. The node anisotropies destroy the conventional picture of (anti)parallel spin and wave vector of a Weyl fermion. This also holds for the Berry curvature around a node, while the monopole charges are independent as integrated quantities. The pairing of the nodes strongly modify the spin texture and the Berry curvature for wave vectors in between the two nodes. Spin components may change their orientation. Integrals over planes perpendicular to the connection line yield finite Zak phases and winding numbers for planes between the two nodes, thereby indicating the topological character.

Electronic properties and lattice dynamics of bulk $\varepsilon$-GaSe and mono-, bi- and tri-tetralayer GaSe are investigated by means of density functional and density functional perturbation theory. The few-tetralayers systems are semiconductors with an indirect nature of the fundamental band gap and a Mexican-hat-shape is observed at the top of the valence band. The phonon branches analysis reveals the dynamical stability for all systems considered together with the LO-TO splitting breakdown in two-dimensional systems. In-plane (E) and out-of-plane (A) zone-center lattice vibrations dominate the Raman and IR spectra.

The use of spatial quantum superpositions of electron states in a gated vdW heterostructure as a charge qubit is presented. We theoretically demonstrate the concept for the ZrSe$_2$/SnSe$_2$ vdW heterostructure using rigorous ab initio calculations. In the proposed scheme, the quantum state is prepared by applying a vertical electric field, is manipulated by short field pulses, and is measured via electric currents. The qubit is robust, operational at high temperature, and compatible with the current 2D technology. The results open up new avenues for the field of physical implementation of qubits., Comment: Main: 6 pages, 5 figures Supporting Information: 5 pages, 3 figures, 2 tables

Absorption and emission of pristine-like semiconducting monolayers of BN, AlN, GaN, and InN are here systematically studied by ab-initio methods. We calculate the absorption spectra for in-plane and out-of-plane light polarization including quasiparticle and excitonic effects. Chemical trends with the cation of the absorption edge and the exciton binding are discussed in terms of the band structures. Exciton binding energies and localization radii are explained within the Keldysh model for excitons in two dimensions. The strong excitonic effects are due to the interplay of low dimensionality, confinement effects, and reduced screening. We find exciton radiative lifetimes ranging from tenths of picoseconds (BN) to tenths of nanoseconds (InN) at room temperature, thus making 2D nitrides, especially InN, promising materials for light-emitting diodes and high-performance solar cells.

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.

Transition metal monopnictides represent a new class of topological semimetals with low-energy excitations, namely, Weyl fermions. We report optical properties across a wide spectral energy range for TaAs, TaP, NbAs and NbP, calculated within density functional theory. Spectra are found to be somewhat independent of the anion and the light polarization. Their features are explained in terms of the upper $s$, $p$, $d$, and $f$ electrons. Characteristic absorption features are related to the frequency dependence of the Fresnel reflectivity. While the lower part of the energy loss spectra is dominated by plasmonic features, the high-energy structures are explained by interband transitions., Comment: Added reference 21 to "S.-Y. Xu, et al, Science 349, 613 (2015)"

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 $20^\circ$.

The uniaxial stress dependence of the band structure and the exciton-polariton transitions in wurtzite ZnO is thoroughly studied using modern first-principles calculations based on the HSE+G0W0 approach, k p modeling using the deformation potential framework, and polarized photoluminescence measurements. The ordering of the valence bands [A(G7), B(G9), C(G7)] is found to be robust even for high uniaxial and biaxial strains. Theoretical results for the uniaxial pressure coefficients and splitting rates of the A, B, and C valence bands and their optical transitions are obtained including the effects of the spin-orbit interaction. The excitonic deformation potentials are derived and the stress rates for hydrostatic pressure are determined based on the results for uniaxial and biaxial stress. In addition, the theory for the stress dependence of the exchange interaction and longitudinal-transversal splitting of the exciton-polaritons is developed using the basic exciton functions of the quasi-cubic approximation and taking the interaction between all exciton states into account. It is shown that the consideration of these effects is crucial for an accurate description of the stress dependence of the optical spectra in ZnO. The theoretical results are compared to polarized photoluminescence measurements of different ZnO substrates as function of uniaxial pressure and experimental values reported in the literature demonstrating an excellent agreement with the computed pressure coefficients., Comment: 16 pages with 9 figures and 5 tables

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.

In many-body perturbation theory (MBPT) the self-energy \Sigma=iGW\Gamma plays the key role since it contains all the many body effects of the system. The exact self-energy is not known; as first approximation one can set the vertex function \Gamma to unity which leads to the GW approximation. The latter properly describes the high-density regime, where screening is important; in the low-density regime, instead, other approximations are proposed, such as the T matrix, which describes multiple scattering between two particles. Here we combine the two approaches. Starting from the fundamental equations of MBPT we show how one can derive the T-matrix approximation to the self-energy in a common framework with GW. This allows us to elucidate several aspects of this formulation, including the origin of, and link between, the electron-hole and the particle-particle T matrix, the derivation of a screened T matrix, and the conversion of the T matrix into a vertex correction. The exactly solvable Hubbard molecule is used for illustration., Comment: 15 pages, 7 figures

We present a universal approach for determining the spontaneous polarization Psp of a wurtzite semiconductor from the emission energies of excitons bound to the different types of stacking faults in these crystals. Employing micro-photoluminescence and cathodoluminescence spectroscopy, we observe emission lines from the intrinsic and extrinsic stacking faults in strain-free GaN micro-crystals. By treating the polarization sheet charges associated with these stacking faults as a plate capacitor, Psp can be obtained from the observed transition energies with no additional assumptions. Self-consistent Poisson-Schroedinger calculations, aided by the microscopic electrostatic potential computed using density-functional theory, lead to nearly identical values for Psp. Our recommended value for Psp of GaN is -0.022+/-0.007 C/m^{2}., Comment: 5 pages, 5 figures