Inelastic Helium Atom Research Articles

The Electron–Phonon Interaction at Vicinal Metal Surfaces Measured with Helium Atom Scattering

Recently, it was demonstrated that inelastic helium atom scattering from conducting surfaces provides a direct measurement of the surface electron–phonon coupling constant (mass enhancement factor λ) via the temperature or the incident wave vector dependence of the Debye–Waller exponent. Here, previous published as well as unpublished helium atom scattering diffraction data from the vicinal surfaces of copper (Cu(11α), with α = 3, 5, 7) and aluminum (Al(221) and Al(332)) were analyzed to determine λ. The results suggested an enhancement with respect to the corresponding data for the low-index surfaces (111) and (001) above the roughening transition temperature. The specific role of steps compared to that of terraces is briefly discussed.

Inelastic helium atom scattering from Sb2Te3(111): phonon dispersion, focusing effects and surfing.

We present an experimental study of inelastic scattering processes on the (111) surface of the topological insulator Sb2Te3 using helium atom scattering. In contrast to other binary topological insulators such as Bi2Se3 and Bi2Te3, Sb2Te3 is much less studied and the as-grown Sb2Te3 sample turns out to be p-doped, with the Fermi-level located below the Dirac-point as confirmed by angle-resolved photoemission spectroscopy. We report the surface phonon dispersion along both high symmetry directions in the energy region below 11 meV, where the Rayleigh mode exhibits the strongest intensity. The experimental data is compared with a study based on density functional perturbation theory calculations, providing good agreement except for a set of additional peculiar inelastic events below the Rayleigh mode. In addition, an analysis of angular scans with respect to a number of additional inelastic events is presented, including resonance enhancement, kinematical focusing, focused inelastic resonance and surfing. In the latter case, phonon-assisted adsorption of the incident helium atom gives rise to a bound state where the helium atom rides the created Rayleigh wave.

Terahertz surface modes and electron-phonon coupling on Bi2Se3 (111)

We present a combined experimental and theoretical study of the surface vibrational modes of the topological insulator (TI) Bi$_2$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 paramenter $\lambda$ = 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 THz measurements on 2D materials as well as the investigation of subtle details (band bending, the presence of quantum well states) with respect to the electron-phonon coupling.

Bending Rigidity of 2D Silica.

A chemically stable bilayers of SiO_{2} (2D silica) is a new, wide band gap 2D material. Up till now graphene has been the only 2D material where the bending rigidity has been measured. Here we present inelastic helium atom scattering data from 2D silica on Ru(0001) and extract the first bending rigidity, κ, measurements for a nonmonoatomic 2D material of definable thickness. We find a value of κ=8.8 eV±0.5 eV which is of the same order of magnitude as theoretical values in the literature for freestanding crystalline 2D silica.

Resolving localized phonon modes on graphene/Ir(111) by inelastic atom scattering

Low energy (few meV) acoustic phonon modes of graphene/Ir (111) have been measured using inelastic helium atom scattering (HAS). The data clearly show two vibrational modes with energies 4.6 and 7.2 meV at Γ¯ with dispersionless branches due to Umklapp scattering. The phonons observed are not the ones expected for a free-standing graphene monolayer, in spite of the weak interaction between graphene and Ir (111). The measured parabolic dispersion of the flexural mode along the ΓM¯ direction allows determining the bending rigidity κ=(0.80±0.07)eV. Inelastic HAS measured at diffraction conditions proves that the moiré superstructure results in localized phonon modes related to the upper and the lower regions of the graphene superstructure. Our study shows that inelastic HAS is suitable to resolve low-energy vibrations spatially localized on structures in the nanometer range.

Ab-initio calculation of surface phonons at the Sb2Te3(111) surface

Density functional perturbation theory is used to study the phonon dispersion relations at the (111) surface of the topological insulator Sb2Te3. Inelastic Helium atom scattering experiments at the (111) surface of the similar Bi2Se3 topological insulator suggested the occurrence of a deep Kohn anomaly related to the presence of the topological surface metallic state. A slab made of three Sb2Te3 quintuple layers is used here to model the (111) surface. This geometry is shown to be sufficient to generate metallic Dirac surface states in good agreement with experimental data from Angle Resolved Photoemission Spectroscopy. The inclusion of spin-orbit interaction in the calculations of surface phonons at wavevectors corresponding to Fermi surface nesting inside the Dirac cone allow us to address the possible occurrence of a Kohn anomaly in Sb2Te3(111) as well. No evidence is found in our calculations for any Kohn anomaly in Sb2Te3 due to electronic transitions across the Dirac cone.

Surface lattice dynamics and electron-phonon interaction in cesium ultra-thin films.

The phonon dispersion curves of ultrathin films of Cs(110) on Pt(111) measured with inelastic helium atom scattering (HAS) are reported and compared with density-functional perturbation theory (DFPT) calculations. The combined HAS and DFPT analysis also sheds light on the bulk phonon dynamics of bcc-Cs, on which very little is known from neutron scattering due to its large neutron capture cross-section. Moreover the temperature dependence of the elastic HAS Debye-Waller exponent of Cs(110)/Cu(111) ultrathin films allows for an estimation of the electron-phonon coupling strength λ as a function of the film thickness.

Surface Dynamics of the Wetting Layers and Ultrathin Films on a Dynamic Substrate: (0.5–4) ML Pb/Cu(111)

The growth of Pb ultrathin films on Cu(111) has been long studied in connection with electronic quantum-size effects and for the different temperature-dependent growth kinetics. At low temperature the formation of a wetting layer (1 monolayer (ML)), is followed by an instability of the 2 ML film and a regular layer-by-layer growth is then only observed for more than two monolayers. The 2 ML film was, however, shown to be stabilized by alloying Pb with 20% Tl. This work presents a theoretical study of the dynamics of the wetting layer as well as for 2 ML Pb0.8Tl0.2, 3 and 4 ML Pb on Cu(111) in the 4 × 4 commensurate phase, for which detailed inelastic Helium atom scattering (HAS) spectra have been measured. The present calculations based on the embedded atom method (EAM) include the dynamics of the substrate. Besides leading to a detailed interpretation of the HAS experimental data, the present results are compared with a previous density-functional perturbation theory (DFPT) study for 3 to 7 ML Pb on a ri...

Observation of Localized Vibrational Modes of Graphene Nanodomes by Inelastic Atom Scattering.

Inelastic helium atom scattering (HAS) is suitable to determine low-energy (few meV) vibrations spatially localized on structures in the nanometer range. This is illustrated for the nanodomes that appear often on graphene (Gr) epitaxially grown on single crystal metal surfaces. The nature of the inelastic losses observed in Gr/Ru(0001) and Gr/Cu/Ru(0001) has been clarified by intercalation of Cu below the Gr monolayer, which decouples the Gr layer from the Ru substrate and changes substantially the out-of-plane, flexural phonon dispersion of epitaxial Gr, while maintaining the nanodomes and their localized vibrations. He diffraction proves that the Cu-intercalated Gr layer is well ordered structurally, while scanning tunneling microscopy reveals the persistence of the (slightly modified) periodic array of Gr nanodomes. A simple model explains the order of magnitude of the energy losses associated with the Gr nanodomes and their size dependence. The dispersionless, low-energy phonon branches may radically alter the transport of heat in intercalated Gr.

Vibrational dynamics and band structure of methyl-terminated Ge(111).

A combined synthesis, experiment, and theory approach, using elastic and inelastic helium atom scattering along with ab initio density functional perturbation theory, has been used to investigate the vibrational dynamics and band structure of a recently synthesized organic-functionalized semiconductor interface. Specifically, the thermal properties and lattice dynamics of the underlying Ge(111) semiconductor crystal in the presence of a commensurate (1 × 1) methyl adlayer were defined for atomically flat methylated Ge(111) surfaces. The mean-square atomic displacements were evaluated by analysis of the thermal attenuation of the elastic He diffraction intensities using the Debye-Waller model, revealing an interface with hybrid characteristics. The methyl adlayer vibrational modes are coupled with the Ge(111) substrate, resulting in significantly softer in-plane motion relative to rigid motion in the surface normal. Inelastic helium time-of-flight measurements revealed the excitations of the Rayleigh wave across the surface Brillouin zone, and such measurements were in agreement with the dispersion curves that were produced using density functional perturbation theory. The dispersion relations for H-Ge(111) indicated that a deviation in energy and lineshape for the Rayleigh wave was present along the nearest-neighbor direction. The effects of mass loading, as determined by calculations for CD3-Ge(111), as well as by force constants, were less significant than the hybridization between the Rayleigh wave and methyl adlayer librations. The presence of mutually similar hybridization effects for CH3-Ge(111) and CH3-Si(111) surfaces extends the understanding of the relationship between the vibrational dynamics and the band structure of various semiconductor surfaces that have been functionalized with organic overlayers.

Polar catastrophe and the structure ofKTa1−xNbxO3surfaces: Results from elastic and inelastic helium atom scattering

The structure and dynamics of cleaved $(001)$ surfaces of potassium tantalates doped with niobium, $\mathrm{KT}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{N}{\mathrm{b}}_{x}{\mathrm{O}}_{3}$ (KTN), with $x$ ranging from $0%$ to $30%$, were measured by helium atom scattering (HAS). Through HAS time-of-flight (TOF) experiments, a dispersionless branch (Einstein phonon branch) with energy of $13\ensuremath{-}14\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ was observed across the surface Brillouin zone in all samples. When this observation is combined with the results from earlier experimental and theoretical studies on these materials, a consistent picture of the stable surface structure emerges: After cleaving the single-crystal sample, the surface should be composed of equal areas of KO and $\mathrm{Ta}{\mathrm{O}}_{2}/\mathrm{Nb}{\mathrm{O}}_{2}$ terraces. The data, however, suggest that ${\mathrm{K}}^{+}$ and ${\mathrm{O}}^{2\ensuremath{-}}$ ions migrate from the bulk to the surface, forming a charged KO lattice that is neutralized primarily by additional ${\mathrm{K}}^{+}$ ions bridging pairs of surface oxygens. This structural and dynamic modification at the $(001)$ surface of KTN appears due to its formally charged $\mathrm{KO}(\ensuremath{-}1)$ and $\mathrm{Ta}{\mathrm{O}}_{2}/\mathrm{Nb}{\mathrm{O}}_{2}(+1)$ layers and avoids a ``polar catastrophe.'' This behavior is contrasted with the $(001)$ surface behavior of the fluoride perovskite $\mathrm{KMn}{\mathrm{F}}_{3}$ with its electrically neutral KF and $\mathrm{Mn}{\mathrm{F}}_{2}$ layers.

Surface Dynamics of Xe(111): An Ambiguous Nobility

A new analysis of inelastic helium atom scattering (HAS) data for the (111) surface of Xe reveals a surprising similarity between the surface phonon dispersion curves of the solid noble gas xenon and of the noble metal copper, the only difference being an energy scale factor. Even more surprising is that the poorly understood X phonon branch observed in Xe(111) actually corresponds to the subsurface S2 phonon branch of Cu(111). A subsurface phonon in a closed-shell insulator surface should not be detectable by HAS, as is instead the case for free electron surfaces, where the electron–phonon interaction can couple the scattering He atoms to phonons several layers beneath the surface (quantum sonar effect). A density functional perturbation theory analysis shows that the large atomic polarizability of surface Xe atoms actually provides the electron–phonon coupling sufficient to explain the comparatively large HAS intensity from the S2 branch of Xe(111). It is concluded that the possibility of directly measu...

Hybridization of surface waves with organic adlayer librations: a helium atom scattering and density functional perturbation theory study of methyl-Si(111).

The interplay of the librations of a covalently bound organic adlayer with the lattice waves of an underlying semiconductor surface was characterized using helium atom scattering in conjunction with analysis by density functional perturbation theory. The Rayleigh wave dispersion relation of CH3- and CD3-terminated Si(111) surfaces was probed across the entire surface Brillouin zone by the use of inelastic helium atom time-of-flight experiments. The experimentally determined Rayleigh wave dispersion relations were in agreement with those predicted by density functional perturbation theory. The Rayleigh wave for the CH3- and CD3-terminated Si(111) surfaces exhibited a nonsinusoidal line shape, which can be attributed to the hybridization of overlayer librations with the vibrations of the underlying substrate. This combined synthetic, experimental, and theoretical effort clearly demonstrates the impact of hybridization between librations of the overlayer and the substrate lattice waves in determining the overall vibrational band structure of this complex interface.

Surface and subsurface phonons of Bi(111) measured with helium atom scattering

The surface phonon dispersion curves of Bi(111) have been measured by inelastic helium atom scattering (HAS) along the two symmetry directions. The complex set of observed dispersion curves, including several branches in the acoustic region, plus a localized and a resonant branch in the optical region, is interpreted by means of calculations based on density functional perturbation theory (DFPT). It is recognized that the upper phonon branches in the acoustic region starting at about $5.3$ meV and $4.3$ meV at zero wave vector correspond to shear-vertical and longitudinal modes localized on the third surface layer (second bilayer), respectively. The HAS ability of detecting subsurface phonons previously observed for Pb(111) multilayers is attributed to the comparatively strong electron-phonon interaction, and confirmed through a DFPT calculation of the phonon-induced surface charge-density oscillations. A comparison of the integrated HAS intensities with those of Pb(111) multilayers measured under similar kinematic conditions allows for an estimation of the electron-phonon mass-enhancement parameter for the Bi(111) surface. An anomaly at the $\overline{\mathrm{M}}$ point, quite sharp at 123 K but very broad at room temperature, is associated with recombination processes of bulk $\overline{\mathrm{M}}$-point pocket electrons with bulk pocket holes at either $\overline{\ensuremath{\Gamma}}$ or equivalent $\overline{\mathrm{M}}$ points.

Electron-Phonon Coupling on the Surface of the Topological InsulatorBi2Se3Determined from Surface-Phonon Dispersion Measurements

In this Letter, we report measurements of the coupling between Dirac fermion quasiparticles (DFQs) and phonons on the (001) surface of the strong topological insulator Bi2Se3. While most contemporary investigations of this coupling have involved examining the temperature dependence of the DFQ self-energy via angle-resolved photoemission spectroscopy measurements, we employ inelastic helium-atom scattering to explore, for the first time, this coupling from the phonon perspective. Using a Hilbert transform, we are able to obtain the imaginary part of the phonon self-energy associated with a dispersive surface-phonon branch identified in our previous work [Phys. Rev. Lett. 107, 186102 (2011)] as having strong interactions with the DFQs. From this imaginary part of the self-energy we obtain a branch-specific electron-phonon coupling constant of 0.43, which is stronger than the values reported from the angle-resolved photoemission spectroscopy measurements.

Mode-Selected Electron-Phonon Coupling in Superconducting Pb Nanofilms Determined from He Atom Scattering

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).

Calculation of inelastic helium atom scattering from H2/NaCl(001)

The one-phonon inelastic low energy helium atom scattering theory is adapted to cases where the target monolayer is a p(1 × 1) commensurate square lattice. Experimental data for para-H(2)/NaCl(001) are re-analyzed and the relative intensities of energy loss peaks in the range 6 to 9 meV are determined. The case of the H(2)/NaCl(001) monolayer for 26 meV scattering energy is computationally challenging and difficult because it has a much more corrugated surface than those in the previous applications for triangular lattices. This requires a large number of coupled channels for convergence in the wave-packet-scattering calculation and a long series of Fourier amplitudes to represent the helium-target potential energy surface. A modified series is constructed in which a truncated Fourier expansion of the potential is constrained to give the exact value of the potential at some key points and which mimics the potential with fewer Fourier amplitudes. The shear horizontal phonon mode is again accessed by the helium scattering for small misalignment of the scattering plane relative to symmetry axes of the monolayer. For 1° misalignment, the calculated intensity of the longitudinal acoustic phonon mode frequently is higher than that of the shear horizontal phonon mode in contrast to what was found at scattering energies near 10 meV for triangular lattices of Ar, Kr, and Xe on Pt(111).

Effects of Film Thickness and Molecular Weight on the Interfacial Dynamics of Atactic Poly(methyl methacrylate)

We have investigated the surface vibrational dynamics at the polymer-vacuum interface of atactic poly(methyl methacrylate) thin films supported on SiO(x)/Si(100) as a function of film thickness and molecular weight. The highly surface-sensitive and nondestructive technique of inelastic helium atom scattering probes the vibrational dynamics at the true polymer-vacuum interface due to the lack of helium atom penetration into the film. For higher molecular weight samples (350 kg/mol), scattering spectra differ between films of thicknesses of fractions of the bulk radius of gyration compared with thicker films due to substrate interactions. A difference in the line shape of the scattering spectra is also present for lower molecular weight samples (60 kg/mol) compared with the thick, higher molecular weight samples. The differences in scattering spectra indicate a reduction of interfacial surface vibrational motion for both the thin, high molecular weight, and low molecular weight films as compared to thick, high molecular weight films. Our experiments demonstrate that dynamics at the interface of polymer thin films are unchanging until the films are thin enough for substrate interactions to influence vibrations at the true interface.

Polymer surface and thin film vibrational dynamics of poly(methyl methacrylate), polybutadiene, and polystyrene

Inelastic helium atom scattering has been used to investigate the vibrational dynamics at the polymer vacuum interface of poly(methyl methacrylate), polystyrene, and polybutadiene thin films on SiO(x)Si(100). Experiments were performed for a large range of surface temperatures below and above the glass transition of these three polymers. The broad multiphonon feature that arises in the inelastic scattering spectra at surface temperatures between 175 and 500 K is indicative of the excitation of a continuum of surface vibrational modes. Similarities exist in the line shapes of the scattering spectra, indicating that helium atoms scatter from groups of similar mass on the surface of these polymer thin films. The line shapes obtained were further analyzed using a semiclassical scattering model. This study has shown that quite different polymer thin films can have similar interfacial dynamics at the topmost molecular layer.

Enhanced creation of dispersive monolayer phonons in Xe∕Pt(111) by inelastic helium atom scattering at low energies

Conditions likely to lead to enhanced inelastic atomic scattering that creates shear horizontal (SH) and longitudinal acoustic (LA) monolayer phonons are identified, specifically examining the inelastic scattering of (4)He atoms by a monolayer solid of XePt(111) at incident energies of 2-25 meV. There is strong inelastic scattering for both dispersive phonon branches (SH and LA) of the monolayer at incident energies below 8 meV. Several improvements enable more complete wave packet calculations of the inelastic scattering than in previous work. Long propagation times are made feasible by adding an absorbing potential at large distance. The times now extend to beyond 100 ps and enable a clarification of processes involving transient trapping of the He atoms. The wave packet is made more monochromatic by significantly increasing the spatial width of the initial Gaussian shape. The narrower energy distribution in the incident beam then enables a demonstration of strong energy dependence of the scattering over a scale of less than 0.3 meV.