Thermodynamic and electronic properties of $({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x{)}_2{\mathrm{Se}}_3$ topological insulator alloy

We present a theoretical study of the structural, electronic, and topological properties of the ternary alloy $({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x{)}_2{\mathrm{Se}}_3$ at the rhombohedral phase through the generalized quasichemical approximation (GQCA) statistical approach and first-principles calculations, including approximate quasiparticle corrections with density functional theory (DFT)-1/2 method. Our results predict good miscibility along the entire composition range. The system exhibits an increase in the inverted energy gap with the increase of the antimony concentration in the alloy. We predict a maximum band gap of 0.28 eV for the Sb concentration $x=0.7$, as well its variation along the entire alloy composition. The inversion of the atomic orbital character of the valence and conduction band is observed for any considered composition, as well nontrivial $Z_2$ topological invariant. The system $({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x{)}_2{\mathrm{Se}}_3$ is a promising candidate to be a topological insulator without topological phase transition, maintaining its topological order with $Z_2=1$ for the entire alloy composition.