Ab initiolattice dynamics and electron-phonon coupling of Bi(111)

Abstract

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.Changes of interatomic couplings are confined mostly to the first two bilayers, resulting in superbulk 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. We give results for the momentumdependent electron-phonon coupling of electronic states belonging to the two surface electronic bands along ΓM which cross the Fermi energy. For larger momenta the lower surface band exhibits a moderate electron-phonon coupling of about 0.45, which is larger than the coupling constant of bulk Bi. For momenta close to Γ, states of both surface bands show even stronger couplings because of interband transitions to bulk states near Γ around the Fermi level. 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.

Lattice Dynamics Study of Elemental Bismuth under High Pressure

“…This in good agreement with our DFT calculations for which one finds at 0 GPa the vibrational frequencies of 71 and 99.7 cm -1 for the A1g and Eg modes. This agrees reasonably well with prior calculations [48][49][50][51][52][53][54] and experiments. [55][56][57][58] Then, with increasing the pressure and under the two experimental conditions, Raman modes of Bi-I phase (Eg and A1g) shift towards globally the lower wavenumber under quasi-hydrostatic conditions and they move slightly to the higher wavenumber under non-hydrostatics conditions.…”

“…Given the exotic nature of some HP crystal structures of elemental Bi such as the host–guest structure Bi-III, a study of their lattice dynamics is notably interesting to understand the guest dynamics in the Bi-III phase, as it can permit a better understanding of the coupling between phonons and electrons, which produces the low-T superconductivity in HP phases of Bi. Until now, the DFT lattice dynamics calculations using different exchange-correlation functionals have focused on the simpler phase I − and only one such calculation was performed on phase V . Only very recently, two new studies have focused on calculations of the lattice dynamics of the Bi-III phase but only using DFT. , The phonon density of states (DOS) has been calculated for the Bi-II phase very recently .…”

Electron-phonon coupling in topological surface states: The role of polar optical modes

“…In particular, phonons and electron-phonon coupling matrix elements are obtained with the efficient linear response technique 29 . This approach has been successfully applied to the renormalization of electronic quasiparticles in bulk 30 , at metal surfaces 31 of spin-orbit split surface states 32 , 33 , and of quantum well states of thin films 34 , 35 .…”

Two-dimensional pnictogens: A review of recent progresses and future research directions

“…Bulk bismuth has a rhombohedral structure containing two Bi atoms per primitive cell with an experimentally determined lattice constant of 4.72 Å [124][125][126] although its free standing monolayer has a lattice constant of 4.33 Å with the vertical distance between the two atomic planes, D ¼ 1.74 Å . 127 While hb-Bi is energetically favorable, it can transform into the metastable planar honeycomb structure.…”