Insights on the electronic and vibrational properties of Bi(111) from first principles

Bi(111) is known to have surface electron carriers close to $\Gamma $ as well as hole carriers at $\Gamma $ and along the $\Gamma $M directions. The lattice dynamics of Bi(111) is however largely unknown. We investigate both the electronic structure and lattice dynamics of Bi(111) films via density-functional-theory and density-functional-perturbation-theory calculations taking into account the spin-orbit coupling (SOC). While the splitting of the branches is dominated by the SOC almost everywhere along the $\Gamma $M direction, around the zone boundary (M), the delocalized character of this state plays an important role. Reducing the thickness of a film decreases the band gap progressively. At $\sim $3-nm thickness, the highest valence band re-crosses the Fermi level and creates extra electron pockets. We find, however, that the lattice dynamics of Bi(111) is robust with respect to film thickness. Bi(111) has a number of ``high-lying'' surface modes in the optical band almost everywhere along the $\Gamma $KM and $\Gamma $M directions, most notably, a vertical mode slightly above the bulk band. Surface acoustic modes are also present as well as some ``low frequency'' optical modes in small regions of the zone. A comparison with recent measurements will be presented, as well as the possible implications on the electron-phonon coupling.