First-principles and spectroscopic studies of Bi(110) films: Thickness-dependent Dirac modes and property oscillations

The electronic structure of Bi(110) thin films as a function of film thickness is investigated by first-principles calculations, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy. Energy minimization in the calculation reveals significant atomic relaxation and rebonding at the surface. The calculated surface energy for the relaxed structures indicates that films consisting of odd numbers of atomic layers are inherently unstable and tend to bifurcate into film domains consisting of neighboring even numbers of atomic layers. This theoretical trend agrees with experimental observations. The results can be explained by the presence of unsaturated pz dangling bonds on the surfaces of films of odd-numbered atomic layers only. These pz dangling bonds form a Dirac-cone feature near the Fermi level at the M¯ point as a consequence of the interplay of mirror symmetry and spin-orbit coupling. Films consisting of even numbers of atomic layers exhibit a band gap at M¯ instead.