Thickness evolution of phonon properties in ultrathin Bi (111) films

Abstract

Ultrathin Bi films have been theoretically predicted to be an elemental two‐dimensional topological insulator recently. Investigation on phonon properties in topological insulators, especially down to a few‐layer regime, is an interesting topic. In this paper, the evolution of structures and phonon properties of ultrathin Bi (111) films with thickness is studied from first‐principles calculations by including spin–orbit coupling. The calculations of lattice dynamics show that both two Raman modes A1g and Eg in ultrathin Bi (111) films harden compared with those in bulk, which is contrary to other nanomaterials. The possible origin of this anomalous phonon behavior is discussed by considering the peculiar semimetallicity of Bi. With increasing thickness, the frequencies of these two Raman modes decrease gradually toward the values in the bulk. Our calculations also show that the softening and hardening of surface phonon modes coexist in ultrathin Bi films.

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 .…”

Ultrafast phonon dynamics of epitaxial atomic layers of Bi on Si(111)

“…High-frequency optical phonon modes were not so well resolved in these experiments. On the other hand, theoretical studies on the two-dimensional Bi(111) films predicted hardening of the A 1g and E g optical phonons at the point, and softening over the rest of the Brillouin zone, with decreasing thickness [18,19]. Their conclusion was contrary to the experimentally observed softening of the A 1g and E g phonons with reducing the size of the Bi nanocrystals [20] and with reducing the thickness of the rhombohedral Bi 2 Se 3 nanoplatelets [21].…”

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

“…Recently, three theoretical studies were devoted to surface phonons in the framework of the density functional theory. 5,25,26 Due to the heavy numerical work involved in dealing with SOC, these calculations were performed only for thin slabs up to 6 bilayers, where the vibrational spectrum exhibited significant variations as a function of thickness. As we are primarily interested in the properties of a semi-infinity Bi(111) surface we checked the convergence of the surface localized vibrations by performing lattice dynamics calculations for 6-and 12-bilayer slabs, respectively.…”

“…Due to the numerical effort to include spin-orbit interaction, only slabs up to 6 bilayers could be treated, 7,23,[27][28][29] , raising the question to what extent the obtained results represent the surface dynamics in the limit of macroscopically thick slabs. For the 6-bilayer calculation, good agreement with the HAS data was found.…”