In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin–orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

The discovery of topological insulators, characterized by an energy gap in bulk electronic band structures and metallic states on boundaries, has greatly inspired studies on the topological properties of the electronic band structures of crystalline materials [...]

We investigate the phase transitions and the properties of the topological insulator in InGaN/GaN and InN/InGaN double quantum wells grown along the [0001] direction. We apply a realistic model based on the nonlinear theory of elasticity and piezoelectricity and the eight-band k·p method with relativistic and nonrelativistic linear-wave-vector terms. In this approach, the effective spin–orbit interaction in InN is negative, which represents the worst-case scenario for obtaining the topological insulator in InGaN-based structures. Despite this rigorous assumption, we demonstrate that the topological insulator can occur in InGaN/GaN and InN/InGaN double quantum wells when the widths of individual quantum wells are two and three monolayers (MLs), and three and three MLs. In these structures, when the interwell barrier is sufficiently thin, we can observe the topological phase transition from the normal insulator to the topological insulator via the Weyl semimetal, and the nontopological phase transition from the topological insulator to the nonlocal topological semimetal. We find that in InGaN/GaN double quantum wells, the bulk energy gap in the topological insulator phase is much smaller for the structures with both quantum well widths of 3 MLs than in the case when the quantum well widths are two and three MLs, whereas in InN/InGaN double quantum wells, the opposite is true. In InN/InGaN structures with both quantum wells being three MLs and a two ML interwell barrier, the bulk energy gap for the topological insulator can reach about 1.2 meV. We also show that the topological insulator phase rapidly deteriorates with increasing width of the interwell barrier due to a decrease in the bulk energy gap and reduction in the window of In content between the normal insulator and the nonlocal topological semimetal. For InN/InGaN double quantum wells with the width of the interwell barrier above five or six MLs, the topological insulator phase does not appear. In these structures, we find two novel phase transitions, namely the nontopological phase transition from the normal insulator to the nonlocal normal semimetal and the topological phase transition from the nonlocal normal semimetal to the nonlocal topological semimetal via the buried Weyl semimetal. These results can guide future investigations towards achieving a topological insulator in InGaN-based nanostructures.

The demand for high-performance displays is continuously increasing because of their wide range of applications in smart devices (smartphones/watches), augmented reality, virtual reality, and naked eye 3D projection. High-resolution, transparent, and flexible displays are the main types of display to be used in future. In the above scenario, the micro-LEDs (light-emitting diodes) display which has outstanding features, such as low power consumption, wider color gamut, longer lifetime, and short response-time, can replace traditional liquid crystal displays and organic LEDs-based display technologies. However, to attain a remarkable position in future display technology, the micro-LEDs need to overcome problems associated with mass transfer and its high cost of manufacturing. Besides micro-LEDs, the other option for future displays includes the usage of color conversion medium (phosphor/ quantum dots) to convert some of the blue light into other colors. In this review, the various mass transfer display technologies and color conversion strategies which are being used for the realization of a full-color display are discussed.

We apply the third-order elasticity theory to study the biaxial relaxation coefficient (the R-B coefficient) in group-III nitride quantum wells and thin films. The R-B coefficient determines the ratio between the out-of-plane and in-plane strain components in these strained layers. We show that the R-B coefficient in four material systems, i.e., AlN thin films grown on AlxGa1-xN substrates, GaN quantum wells grown on AlxGa1-xN substrates, GaN thin films grown on InxGa1-xN virtual substrates, and InN quantum wells grown on InxGa1-xN virtual substrates, to a large extent, depends on the in-plane strain arising from the lattice misfit between the strained layers and the substrates. This phenomenon cannot be described by the linear theory of elasticity. We also find that the R-B coefficient in most of the quantum wells and thin films made of InxGa1-xN and AlxGa1-xN alloys significantly depends on the in-plane strain, which is reflected by the observed discrepancies between the results obtained using third-order elasticity and linear elasticity. These discrepancies are proportional to the magnitude of the in-plane strain for AlxGa1-xN thin films and InxGa1-xN quantum wells grown on GaN substrates and they vanish when Al or In contents are smaller than 0.2. For AlxGa1-xN the quantum wells grown on AlN substrates and InxGa1-xN thin films grown on InN substrates, we find that the discrepancies between the results obtained using third-order elasticity and linear elasticity are not proportional to the in-plane strain. Unusual behaviour of the R-B coefficient in group-III nitride alloys originates from the different values of the elastic constants for the binary nitride semiconductors, causing the opposite dependences of the R-B coefficient on strain for GaN compared to InN and AlN.

We determine the second-order elastic constants (SOECs) and the third-order elastic constants (TOECs) for wurtzite AlN, GaN, and InN using the hybrid-density functional theory calculations with the plane wave basis sets. We apply the analytical formulas for the deformation gradient tensors as functions of the Lagrangian strain in order to eliminate the truncation errors in the Taylor expansion series of the deformation gradients and to facilitate the calculation of the Lagrangian stress. We show that the convergence criteria for the calculation of the TOECs with respect to thek-points density and the plane wave cutoff energy are similar for the strain-energy method and the strain-stress approach. The strain-energy method turns out to be more stable against the numerical errors than the strain-stress approach, which requires smaller tolerance for the precision of the self-consistent calculations. The SOECs, extracted by the method of least squares, are consistent with the experimental data and the previousab initiocalculations. Then, we investigate the biaxial relaxation coefficient for AlN, GaN, and InN, subjected to biaxial stress in the plane perpendicular to thecaxis of the wurtzite structure. This coefficient determines the relationship between the in-plane and out-of-plane strain components in thin films and quantum wells grown onc-plane substrates. We demonstrate that for InN and AlN, the biaxial relaxation coefficient increases significantly with the in-plane strain, whereas it shows the opposite behavior in GaN. These results are well described by the third-order elasticity theory and they cannot be modeled by the linear theory of elasticity, which predicts no dependence of the biaxial relaxation coefficient on the in-plane strain. Therefore, the obtained TOECs should prove very useful for the modelling of strain-related phenomena in heterostructures, nanostructures and devices made of the group-III nitride semiconductors.

We propose a general and easy-to-use method of the ab initio calculation of the higher-order elastic constants, which is based on the analytical formulas for the deformation-gradient tensors as functions of the Lagrangian strain. The method allows for elimination of the truncation errors in the Taylor expansion series of the deformation gradients and is particularly useful to calculate the fourth-order elastic constants, where large strains have to be applied. It also facilitates the calculation of the Lagrangian stress, which is helpful in determination of the strain-stress relations. To demonstrate the application of our approach, we derive the analytic formulas for the deformation gradients as functions of the Lagrangian strain tensors, which are used in calculations of the third-order elastic constants in trigonal crystals and the fourth-order elastic constants in cubic crystals. Then, we perform the ab initio calculations of the fourth-order elastic constants in face-centered-cubic aluminum. We discuss the results obtained using the strain-energy and strain-stress relations and analyze the errors of the fourth-order elastic constants which would be incurred when approximating the deformation gradients by the Taylor polynomials. We show that the relatively small truncation errors in the Taylor expansion series of the deformation gradients can cause significant deviations of the fourth-order elastic constants. This effect is larger for the strain-energy method than for the strain-stress approach. We find that in both methods, the deviations are particularly significant for the ${C}_{1155}$, ${C}_{1266}$, ${C}_{4455}$, ${C}_{1255}$, and ${C}_{1456}$ elastic constants and are mainly caused by the truncation errors in the nondiagonal elements of the Taylor expansion series of the deformation gradients.

We study the influence of negative spin-orbit coupling on the topological phase transition and properties of the topological insulator state in InGaN-based quantum wells grown along c axis of the wurtzite lattice. The realistic eight-band k·p method with relativistic and nonrelativistic linear-k terms is employed. Our calculations show that the negative spin-orbit coupling in InN is not an obstacle to obtain the topological insulator phase in InN/InGaN and InGaN/GaN quantum wells. The bulk energy gap in the topological insulator state can reach 2 meV, which allows experimental verification of the edge state transport in these materials. The topological phase transition occurs due to the band inversion between the highest light hole subband and the lowest conduction subband, and almost always is mediated by the two-dimensional Weyl semimetal, arising from an anticrossing of these subbands at zero in-plane wave vector. However, for certain InGaN/GaN quantum wells, we find that the magnitude of this anticrossing vanishes, leading to the appearance of the Dirac semimetal. The novel transition between the Weyl and Dirac semimetals originates from vanishing of the average in-plane spin-orbit interaction parameter, which decouples the conduction subband from the light hole subband at zero in-plane wave vector.

We study theoretically the topological phase transition and the Rashba spin–orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

We present a theoretical study of the magnetic-field effect on the electronic properties of the two-dimensional, hypothetical topological insulator based on the InN/GaN quantum well system. Using the effective two-dimensional Hamiltonian, we have modelled magneto-transport in mesoscopic, symmetric samples of such materials. It turns out that, as in the case of the other two-dimensional topological insulators, the magnetoconductance in such samples is quantized due to the presence of helical edge states for magnetic fields below a certain critical value and for fairly small disorder strength. However, in our case the helical edge transport is much more prone to the disorder than, for example, in the case of topological insulators based on the HgTe/CdTe quantum wells. At low enough level of disorder and for the Fermi energy located in the energy gap of an infinite planar quantum well, we may expect an interesting phenomenon of non-monotonic dependence of the conductance on the magnetic field caused by the complicated interplay of couplings between the heavy hole, light hole and conduction subbands. Copyright (C) EPLA, 2017.

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

The applicability of the Martin transformation [R. M. Martin, Phys. Rev. B 6, 4546 (1972)] to the elastic constants of wurtzite and zinc-blende group-III nitride alloys is examined using density functional theory calculations. The composition dependencies of the elastic constants in InGaN, AlGaN, and InAlN are determined by means of ab-initio calculations and compared with the results obtained from the Martin's method. A detailed analysis reveals that the Martin transformation can approximate reasonably well the dependence of the elastic constants on composition in wurtzite InGaN alloys, except for the case of C-33 where it predicts too small bowing. However, it fails to reproduce correctly the composition dependencies of C-13 and C-33 in wurtzite InAlN and C-13, C-33, and C-44 in wurtzite AlGaN. In order to identify the origin of the failure of the Martin transformation, the effective elastic constants of strained wurtzite alloys with the ideal value of the lattice axial ratio c/a have been investigated. It is shown that these effective elastic constants are significantly closer to the elastic constants predicted by the Martin's method which indicates that the breakdown of the Martin transformation in group III nitride alloys is partially caused by the deviation of the c/a axial ratio from the ideal value. (C) 2015 AIP Publishing LLC.

We theoretically study the polarization-induced band inversion phenomenon in c-plane In-rich InGaN/GaN quantum wells. Our calculations performed using the k.p method with the 8x8 Rashba Sheka Pikus Hamiltonian for the structures with the indium content between 90% and 100% show that the reordering of the conduction and valence bands occurs for the quantum well widths below the theoretical values of critical thickness for InGaN layers pseudomorphically grown on GaN substrates.

We present a theoretical description of excitonic spectra in GaN-based quantum wells in a wide range of magnetic fields taking into account built-in strain and electric fields, and valence band mixing due to the quantum well confinement. Our calculations performed for the GaN/AlGaN quantum wells reveal a nonlinear behavior of the excitonic Zeeman splitting on magnetic field. We have determined that the low magnetic field g-factor dependence on the quantum well width shows a steplike variation due to the reordering of the light-and heavy-hole valence subbands. Sharp change of the g factor is also predicted for InGaN/GaN quantum wells grown on a virtual metamorphic InGaN substrate.

We investigate the influence of external pressure on optical anisotropy of GaN/ AlxGa1-xN quantum wells (QWs) grown along the c-crystallographic direction. Our theoretical study reveals that for sufficiently narrow GaN/AlxGa1-xN QWs, lattice matched to GaN substrate a pressure-dependent switching of polarization of emitted light occurs. This switching of polarization is manifested by the change of sign of the degree of polarization of photoluminescence spectra. We note that the results of our model critically depend on the deformation potential values and therefore can be used for verification of existing literature values of these parameters.

The deformation potentials a(cz) - D-1, a(ct) - D-2, D-3, D-4, and D-5 are determined for random AlGaN and InGaN alloys using electronic band structure calculations based on the density functional theory. A sublinear composition dependence is obtained for a(cz) - D-1 and D-3 in AlGaN, and D-3 in InGaN, whereas superlinear behavior on composition is found for a(ct) - D-2, D-4, and D-5 in AlGaN, and a(ct) - D-2 and D-5 in InGaN. The optical polarization properties of nitride quantum wells are very well described by the k.p method when the obtained deformation potentials are included. In m-plane AlGaN/AlN and InGaN/GaN quantum wells, the difference between the interband transition energies for light polarized parallel and orthogonal to the crystalline c axis compares more favorably to experimental data, than when deformation potentials previously reported in literature are used.

Elastic properties of wurtzite InxGa1-xN and InxAl1-xN alloys are investigated using the first principles calculations. For alloys with uniform distribution of In atoms, a Vegard-like approximation can describe the composition dependences of C-12, C-13, and C-44 in InxGa1-xN, and C-12, C-13, and C-33 in InxAl1-xN, whereas significant sublinear deviations are found for C-11 and C-33 in InxGa1-xN and for C-11 and C-44 in InxAl1-xN. These deviations lead to significant changes in determination of strain in InxGa1-xN and InxAl1-xN layers grown coherently on GaN substrates along polar and nonpolar directions. Changes of the interband transitions energy in InxGa1-xN/GaN quantum wells due to the inclusion of the nonlinear dependence of the elastic constants on In content do not exceed 25 meV.

We show theoretically that for narrow GaN/AlxGa1-xN quantum wells, lattice matched to GaN substrate and grown along the c-crystallographic direction a pressure-dependent reordering of the topmost valence subbands having different symmetries occurs. This reordering depends critically on the values of the D-3 and D-4 deformation potentials and can be employed in the verification of existing literature values of these parameters. In order to analyze the effect of subband reordering on the the optical properties of such systems we consider a multiband exciton problem including k . p and Coulomb coupling between subbands. Our calculations show that the difference in the exciton binding energies in different valence subbands contributes significantly to the conditions for the reordering of corresponding optical transitions in emission and absorption spectra. Pressure-induced reordering of excitonic transitions leads to a noticeable modification of the polarization of emitted/absorbed light.

We study theoretically the in uence of external hydrostatic pressure on the valence band structure in [0001]-oriented AlxGa1−xN/AlN quantum wells used in deep-ultraviolet light emitting devices. The calculations performed using the multi-band k·p method with excitonic e ects show that for AlxGa1−xN/AlN quantum wells with x = 0.7 and quantum well width of 1.5 nm, reordering of the topmost valence subbands having di erent symmetries occurs with increasing pressure. In these structures, at low pressure values the topmost valence level is of Γ9 symmetry whereas it changes to the Γ7 state for pressures about 2.5 GPa. We also nd that the excitonic e ects increase the critical value of pressure at which the change in the polarization of the emitted light occurs to 7 GPa. This behavior is opposite to the pressure-dependent reordering of the topmost valence band states in thin GaN/AlGaN quantum wells which occurs from Γ7 to Γ9 states. PACS: 78.55.Cr, 78.67.De, 62.50.−p