Surface lattice dynamics and electron-phonon interaction in ultrathin Bi(111) film

The surface phonon and electron-phonon interactions in the two-dimensional topological insulator Bi(111) film are calculated, including the spin-orbit coupling from density-functional perturbation theory. By analyzing the zone-center phonons, an anomalous phonon hardening of two Raman modes, Eg and A1g, in ultrathin films is found and is explained by considering the redistribution of the charge density on the surface of the semimetallic Bi. Surface phonon band structures and the surface phonon density of states are given, and we find that softening and hardening of surface phonon modes occur simultaneously in ultrathin Bi film, but the softening may dominate over the hardening. The calculated electron-phonon coupling constant λ for Bi(111) film is much larger than that for the bulk, which might induce surface-localized superconductivity in this two-dimensional topological insulator.