We present first-principles calculations of the structural and electronic properties of binary GaN, ScN and Sc x Ga 1−x N alloys in the zinc-blende structure using pseudopotential plane-wave method within the density functional theory. The alloys are described by considering configurations in 16-atom supercells, corresponding to 2 × 2 × 2 conventional cubic cells. The lattice parameter, bulk modulus, bulk modulus derivation, the energy band gap and bowing parameter are obtained as a function of Sc concentration for ternary alloys Sc x Ga 1−x N . Our studies focus on the concentration dependence of the electronic band structure and bowing parameter of these alloys. We found that x composition affects strongly bowing parameter and the band gap increases with increasing Sc concentration for Sc x Ga 1−x N in the zinc-blende structure. The results also show that the energy band gap and bowing parameter of the Sc x Ga 1−x N alloys can be obtained by a third-order polynomial equation, E gap (x) = −2.56x 3 + 4.29714x 2 − 0.94857x + 1.83429 eV and b(x) = −72.61x 3 + 117.7x 2 − 70.27x + 16.08 eV, respectively.

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The zincblende ternary alloys TlxGa1−xAs (0 < x < 1) are studied by numerical analysis based on the plane wave pseudopotential method within the density functional theory and the local density approximation. To model the alloys, 16-atom supercells with the 2 × 2 × 2 dimensions are used and the dependency of the lattice parameter, bulk modulus, electronic structure, energy band gap, and optical bowing on the concentration x are analyzed. The results indicate that the ternary TlxGa1−xAs alloys have an average band gap bowing parameter of 4.48 eV for semiconductor alloys and 2.412 eV for semimetals. It is found that the band gap bowing strongly depends on composition and alloying a small Tl content with GaAs produces important modifications in the band structures of the alloys.

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This work discusses the effect of topology in the frame of direct Coulomb interactions, considering two distinct geometries, namely the Hall bar and the Corbino disc. In the mainstream approaches to the quantized Hall effect, the consequences of interactions are usually underestimated. Here, we investigate the electron number density, potential and current distributions within the screening theory that considers electron-electron interactions. Inclusion of direct Coulomb interaction and realistic boundary conditions result in local metal-like compressible and (Topological) insulatorlike incompressible regions. Consequently, we show that the bulk of both geometries in coordinate space is not incompressible throughout the quantized Hall plateau. Furthermore, placing two inner contacts within the Hall bar geometry shows that the quantization is unaffected by changing the genus number in real space. Finally, we propose novel experiments which will enable us to distinguish the topological properties of the two geometries in the configuration space.