Third-order elastic constants and biaxial relaxation coefficient in wurtzite group-III nitrides by hybrid-density functional theory calculations.

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.

Topological insulator with negative spin-orbit coupling and transition between Weyl and Dirac semimetals in InGaN-based quantum wells.

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.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure.

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.