A comparative study of topological electronic structures of bilayers of group IV and V atoms

The topological electronic structures of free-standing bilayers of group-IV (C, Si, Ge, Sn, and, Pb) and V (As, Sb, and, Bi) atoms under isotropic strain have been studied using first-principles calculations. For group IV elements, heavier elements with larger spin--orbit coupling possess larger gaps at K, but a lower conduction band at $\Gamma $, making the system metallic. Only a few group-IV bilayers remain insulating due to small gaps at $\Gamma $. In contrast, for group V elements, spin-orbit coupling changes the ordering of bands at $\Gamma $. While As and Sb bilayers are found to be topologically trivial without isotropic strain, strength of spin-orbit coupling in Bi bilayer is large enough to induce band inversions, making the system a topological insulator. Sb bilayer also goes into a topological insulating phase if the spin-orbit coupling is artificially enhanced.