Dependence of the band structure of Bi(111) bilayers on lattice constant and spin-orbit splitting induced by a H monolayer

Abstract

The band structure of free Bi(111) films is studied by means of full-relativistic density functional theory calculations. A single free Bi(111) bilayer with optimized lattice constant a = 4.19 Å is found to be semiconducting both in semirelativistic and full-relativistic calculations, i.e. without and with accounting for spin–orbit coupling (SOC), respectively. With increases of a up to the related bulk value, 4.53 Å, the gap decreases down to ∼0.06 eV. For a up to 4.60 Å the band gap, calculated with SOC is significantly less than that without SOC, meaning that SOC does not open the gap, but, in contrast, decreases it. For the bilayer with a = 4.70 Å the situation is opposite and the gap opens just due to SOC. For larger a, free Bi(111) bilayers are semiconducting regardless of accounting for SOC. Thicker films, built from several Bi(111) bilayers, in contrast, acquire semimetallic properties. It is suggested therefore that the metallicity of Bi slabs stems from the interaction between Bi bilayers but not from surface states. A hydrogen monolayer, adsorbed on one face of the Bi(111) film, leads to the appearance of spin–orbit splitting of the bands. For clean Bi(111) slabs, the splitting is absent, which means that the existence of the surface itself cannot initiate the required break of inversion symmetry.