The electron-phonon coupling (EPC) strength for each phonon mode in superconducting Pb films is measured by inelastic helium atom scattering (IHAS). This surprising ability of IHAS relies on two facts: (a)~In ultrathin metal films, the EPC range exceeds the film thickness, thus enabling IHAS to detect most film phonons, even 1~nm below the surface; (b)~IHAS scattering amplitudes from single phonons are shown, by first-principle arguments, to be proportional to the respective EPC strengths. Thus IHAS is the first experiment providing mode-selected EPC strengths (mode-lambda spectroscopy).

This paper presents material properties particularly suited to be measured with helium scattering techniques. Below a specific science case example illustrating the measurement of the electron–phonon coupling constant λ on a topological insulator surface.

The quasi two-dimensional electron gas on a metal film can transmit to the surface even minute mechanical disturbances occurring in the depth, thus allowing the gentlest of all surface probes, helium atoms, to perceive the vibrations of the deepest atoms via the induced surface-charge density oscillations. A density functional perturbation theory (DFPT) and a helium atom scattering study of the phonon dispersion curves in lead films of up to 7 mono-layers on a copper substrate show that: (a) the electron–phonon interaction is responsible for the coupling of He atoms to in-depth phonon modes; and (b) the inelastic HAS intensity from a given phonon mode is proportional to its electron–phonon coupling. The direct determination of mode-selected electron–phonon coupling strengths has great relevance for understanding superconductivity in thin films and two-dimensional systems.

A prominent surface acoustic wave dominates the vibrational dynamics of Bi ₂ Te ₃ (111). Theoretical calculations reveal the crucial role of vdW interactions.

We present a combined experimental and theoretical study of the surface vibrational modes of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ with particular emphasis on the low-energy region below 10 meV that has been difficult to resolve experimentally. By applying inelastic helium atom scattering (HAS), the entire phonon dispersion was determined and compared with density functional perturbation theory (DFPT) calculations. The intensity of the phonon modes is dominated by a strong Rayleigh mode, in contrast to previous experimental works. Moreover, also at variance with recent reports, no Kohn anomaly is observed. These observations are in excellent agreement with DFPT calculations. Besides these results, the experimental data reveal—via bound-state resonance enhancement—two additional dispersion curves in the gap below the Rayleigh mode. They are possibly associated with an excitation of a surface electron density superstructure that we observe in HAS diffraction patterns. The electron-phonon coupling parameter $\lambda =0.23$, derived from our temperature-dependent Debye-Waller measurements, compares well with values determined by angular resolved photoemission or Landau level spectroscopy. Our work opens up a new perspective for terahertz (THz) measurements on two-dimensional (2D) materials as well as the investigation of subtle details (band bending, the presence of a 2D electron gas) with respect to the electron-phonon coupling.

The vibrational properties of ultrathin Bi(111) films have been calculated by applying density functional perturbation theory with and without the inclusion of spin-orbit interaction. Phonon dispersion curves of dynamically stable bilayers are presented and analyzed. Surprisingly, the Rayleigh mode is found to have the largest amplitude on the second atomic layer. Moreover an optical surface phonon branch is found to be localized above the optical band and confined within the first surface bilayer. The analysis of this mode as a function of the number of bilayers allows one to estimate the contribution of the spin-orbit coupling to the electron-phonon interactions.DOI: http://dx.doi.org/10.1103/PhysRevB.87.075412Received 8 November 2012Published 7 February 2013©2013 American Physical Society