The Electron–Phonon Interaction of Low‐Dimensional and Multi‐Dimensional Materials from He Atom Scattering

Abstract

Atom scattering is becoming recognized as a sensitive probe of the electron–phonon interaction parameter λ at metal and metal‐overlayer surfaces. Here, the theory is developed, linking λ to the thermal attenuation of atom scattering spectra (in particular, the Debye–Waller factor), to conducting materials of different dimensions, from quasi‐1D systems such as W(110):H(1 × 1) and Bi(114), to quasi‐2D layered chalcogenides, and high‐dimensional surfaces such as quasicrystalline 2ML‐Ba(0001)/Cu(001) and d‐AlNiCo(00001). Values of λ obtained using He atoms compare favorably with known values for the bulk materials. The corresponding analysis indicates in addition, the number of layers contributing to the electron–phonon interaction, which is measured in an atom surface collision.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

“…The HAS diffraction spectra of Bi (114) along the row direction, reported in [15,16], show the temperature evolution of the CDW peaks, the most prominent being that at (±3/2,0); an example, measured at 113 K, is shown in Figure 5d. The best fit of the order parameter, proportional to [I CDW (T)/I CDW (0)] 1/2 for the CDW peak (inset of Figure 5d), yields a CDW critical temperature of 242 ± 7 K and a critical exponent β = 0.32 ± 0.03, consistent with the universal exponent of 1/3 as predicted in the presence of fluctuations [40,41], and in agreement with the critical exponent for other CDWs in layered chalcogenides and quasi-1D systems [17,[42][43][44][45].…”

“…A slightly larger value for Bi (114), λ = 0.45, is obtained when treated as a 1D free-electron gas system, as discussed in Ref. [17]. This value is probably more reliable, in consideration of the quasi-1D metallic nature of Bi (114)(1 × 2), although the difference is well within the uncertainty of the present method.…”

Material properties particularly suited to be measured with helium scattering: selected examples from 2D materials, van der Waals heterostructures, glassy materials, catalytic substrates, topological insulators and superconducting radio frequency materials

“…Due to the heavy elements in typical TIs such as Bi 2 Se 3 , the energies of (acoustic) surface lattice vibrations are typically in the low meV energy region and thus measurements of the surface phonon dispersion require high energy resolution as well as surface sensitive probes. HAS provides also access to the e-ph coupling strength at surfaces 9,149 (see Section 3.2.1), a quantity that determines energy losses in surface electronic transport. While scattering from defects and other lattice imperfections can possibly be controlled by the quality and a careful growth of crystals and films, phonons will be excited in even the most perfect crystals.…”

“…Furthermore, HAS can detect subsurface phonons as deep as the range of e-ph interaction, allowing investigations of the phonon dispersion curves and their e-ph interaction not only at surfaces but also in ultra-thin films. 28,149,165 The possibility of observing the dispersion and knowing the e-ph coupling of waves localised at the interface of supported ultra-thin films, 86 subsurface layers 166 or optical branches in Bi 2 Te 3 and Bi 2 Se 3 155 opens the prospect of developing an interface or sub-surface phononics, thus avoiding contamination problems which would affect surface acoustic wave devices in the THz domain.…”

Inter-adsorbate forces and coherent scattering in helium spin-echo experiments

“…Thus, the technique is particularly powerful in analysing vibrations that have weight at, or near, the surface. [2][3][4] The resulting inelastic scattering gives both the energy and wavelength dependence of the excitations. Helium atoms are also sensitive to changes in the electron density as adsorbed atoms and molecules move on an otherwise flat surface.…”