  We present a comprehensive ab initio study of structural, electronic, lattice
dynamical and electron-phonon coupling properties of the Bi(111) surface within
density functional perturbation theory. Relativistic corrections due to
spin-orbit coupling are consistently taken into account. As calculations are
carried out in a periodic slab geometry, special attention is given to the
convergence with respect to the slab thickness. Although the electronic
structure of Bi(111) thin films varies significantly with thickness, we found
that the lattice dynamics of Bi(111) is quite robust and appears converged
already for slabs as thin as 6 bilayers. Changes of interatomic couplings are
confined mostly to the first two bilayers, resulting in super-bulk modes with
frequencies higher than the optic bulk spectrum, and in an enhanced density of
states at lower frequencies for atoms in the first bilayer. Electronic states
of the surface band related to the outer part of the hole Fermi surfaces
exhibit a moderate electron-phonon coupling of about 0.45, which is larger than
the coupling constant of bulk Bi. States at the inner part of the hole surface
as well as those forming the electron pocket close to the zone center show much
increased couplings due to transitions into bulk projected states near
Gamma_bar. For these cases, the state dependent Eliashberg functions exhibit
pronounced peaks at low energy and strongly deviate in shape from a Debye-like
spectrum, indicating that an extraction of the coupling strength from measured
electronic self-energies based on this simple model is likely to fail.
