The mechanical properties of two-dimensional materials are important for a wide range of applications including composite and van der Waals-materials, flexible electronics and superconductivity. Several aspects are highly debated in the literature: For example, the theoretically predicted bending rigidity x at 0 K for quasi free-standing graphene varies from 0.8 to 1.6 eV, and there are predictions that it could either increase or decrease with temperature. Here we present an experimental study of the temperature-dependent bending rigidity x(T) of graphene. From the phonon dispersion relation measured with helium atom scattering for the out-of-plane acoustic (ZA) mode, we find x(T) to increase with sample temperature. We compare our experimental results with novel molecular dynamics (MD) simulations performed as part of this study as well as available literature data. The calculations reproduce the temperature trend of our experiments, but with a slightly weaker slope. A probable cause for the observed differences is the slight strain associated with experimental substrate supported graphene that is not present in the calculations.

The electron-phonon interaction (or mass-enhancement (ME) factor) at the hydrogen-covered (110) surface of Mo1-x Re x alloys has been derived for three different Re concentrations, x = 0.05, 0.15, 0.25, from the incident-energy dependence of Helium atom scattering (HAS) intensities. It is shown that the ME factor may also be extracted, in the case of stepped surfaces, from the maxima of the drift spectra, as well as from the intensities of the diffuse elastic peak and of the inelastic scattering from Rayleigh waves. It is confirmed that the ME factor, and therefore the superconducting critical temperature, increase with Re concentration, together with the charge-density wave gap occurring in the hole-electron dispersion curve of the quasi-one-dimensional free electron gas, observed long ago with inelastic HAS in H-covered Mo1-x Re x alloys.

The boson peak was recently detected experimentally for the first time in a 2D material (bilayer silica). The experiment was performed using helium atom scattering. Here we apply helium atom scattering in further experimental investigations of the presence of the boson peak in 2D materials. We investigate two crystalline 2D materials (graphene and AB-bilayer graphene) as well as one amorphous 2D material: a 2D silica sample containing nanoscale holes, thus displaying a different mass density from the 2D silica investigated in the previously published experiment. The crystalline materials graphene and bilayer graphene show no indication of the presence of a boson peak. The boson peak in the bilayer silica containing a random distribution of holes is identified at 7 +/- 1 meV, which is within the error bars of the value for the first bilayer silica sample previously investigated.

Previously, helium atom scattering (HAS) has been shown to probe the electron–phonon interaction at conducting crystal surfaces via the temperature dependence of the specular peak intensity. This method is now extended to non-stoichiometric superconductors. The electron–phonon interaction, as expressed by the mass-enhancement factor λ, is derived from the temperature dependence of the diffuse elastic scattering intensity, which specifically depends on the non-stoichiometric component responsible for superconductivity. The measured value of the mass-enhancement factor for Bi2Sr2CaCu2O8+δ at the optimal doping δ = 0.16 is λ = 0.55 ± 0.08 is in good agreement with values of λ recently estimated with other methods. This also confirms the relevant role of electron–phonon interaction in high-temperature non-stoichiometric cuprate superconductors.

Nanoscale thin film coatings and surface treatments are ubiquitous across industry, science, and engineering; imbuing specific functional or mechanical properties (such as corrosion resistance, lubricity, catalytic activity and electronic behaviour). Non-destructive nanoscale imaging of thin film coatings across large (ca. centimetre) lateral length scales, crucial to a wide range of modern industry, remains a significant technical challenge. By harnessing the unique nature of the helium atom-surface interaction, neutral helium microscopy images these surfaces without altering the sample under investigation. Since the helium atom scatters exclusively from the outermost electronic corrugation of the sample, the technique is completely surface sensitive. Furthermore, with a cross-section that is orders of magnitude larger than that of electrons, neutrons and photons, the probe particle routinely interacts with features down to the scale of surface defects and small adsorbates (including hydrogen). Here, we highlight the capacity of neutral helium microscopy for sub-resolution contrast using an advanced facet scattering model based on nanoscale features. By replicating the observed scattered helium intensities, we demonstrate that sub-resolution contrast arises from the unique surface scattering of the incident probe. Consequently, it is now possible to extract quantitative information from the helium atom image, including localised ångström-scale variations in topography.

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.

The boson peak is an excess in the phonon vibrational density of states relative to the Debye model. It has been observed in a wide range of amorphous materials, from inorganic glasses to polymers. Two-dimensional random matrix models and molecular dynamics simulations predict that the boson peak should also be present in amorphous two-dimensional materials, a notion that is of practical importance because it leads to an excess of heat capacity and influences transport properties. However, up until now, experimental observations in actual materials have not been possible due to the limited surface sensitivity of the methods usually applied to measure the boson peak. Here we present the experimental evidence of a boson peak in two-dimensional silica, through phonon spectra measured by means of inelastic helium-atom scattering. We identify the boson peak as a wavenumber-independent spectral maximum at a frequency similar to what has been observed in and predicted for bulk vitreous silica. Furthermore, we present a heterogeneous-elastic theory calculation in two dimensions, which shows how the vibrational coupling of the transversal and flexural shear vertical phonon modes produces the boson peak in two-dimensional materials at a frequency similar to that of the bulk, in agreement with our measurements. The boson peak refers to an excess in the phonon density of states seen in three-dimensional amorphous materials. Helium-atom scattering experiments have now revealed a boson peak in a two-dimensional material, too, at a frequency similar to that of the bulk material.

Two dimensional (2D) materials are a young class of materials that is foreseen to play an important role as building blocks in a range of applications, e.g. flexible electronics. For such applications, mechanical properties such as the bending rigidity κ are important. Only a few published measurements of the bending rigidity are available for 2D materials. Nearly unexplored is the question of how the 2D material density influences the bending rigidity. Here, we present helium atom scattering measurements on a "holey" bilayer silica with a density of 1.4 mg m-2, corresponding to 1.7 monolayers coverage. We find a bending rigidity of 6.6 ± 0.3 meV, which is lower than previously published measurements for a complete 2D film, where a value of 8.8 ± 0.5 meV was obtained. The decrease of bending rigidity with lower density is in agreement with theoretical predictions.

The boson peak is an excess in the phonon density of states relative to the Debye Model, which occurs at frequencies below the Debye limit. It is present in most amorphous materials and, as was recently shown, can sometimes be found also in crystals. Here we present first experimental evidence of the boson peak in a 2D material, namely 2D silica (SiO$_2$). The measurements were obtained by helium atom scattering. A dispersionless boson peak is seen at $6 \pm 0.5$ meV (1.5$ \pm$ 0.15 THz) and $-6 \pm 1.5$ meV ($-1.5 \pm 0.4$ THz), with reasonable evidence for a double excitation at $\pm 12 \pm 2.5$ meV ($2.9 \pm 0.6$ THz).

A Profile of Giorgio Benedek written by the Guest Editors of this Festschrift themed collection.

In previous works it has been shown that the Debye-Waller (DW) exponent for Helium atom specular reflection from a conducting surface, when measured as a function of temperature in the linear high-temperature regime, allows for the determination of the surface electron-phonon coupling. However, there exist a number of experimental measurements that exhibit non-linearities in the DW exponent as a function of the surface temperature. Such non-linearities have been suggested as due to vibrational anharmonicity or a temperature dependence of the surface carrier concentration. In this work, it is suggested, on the basis of a few recent experimental data, that the deviations from linearity of the DW exponent temperature-dependence, as observed for conducting surfaces or supported metal overlayers with the present high-resolution He-atom scattering, permit to single out the specific role of high-energy phonons in the surface electron-phonon mass-enhancement factor.

Many experiments that utilize beams of incident atoms colliding with surfaces as a probe of surface properties are carried out at large energies, high temperatures and with large mass atoms. Under these conditions the scattering process does not exhibit quantum mechanical properties such as diffraction or single-phonon excitation, but rather can be treated with classical physics. This is a review of work carried out by the authors over a span of several years to develop theoretical frameworks using classical physics for describing the scattering interactions of atom with surfaces.

This themed collection includes a collection of articles on new trends and challenges in surface phenomena, carbon nanostructures and helium droplets.

An atomic projectile colliding with a surface at kinetic energies in the thermal or hyperthermal range interacts with and is reflected by the electronic density well in front of the first layer of target atoms, and it is generally accepted that the repulsive interaction potential is proportional to the density of electrons extending outside the surface. This review develops a complete treatment of the elastic and inelastic scattering of atoms from a conducting surface in which the interaction with the electron density and its vibrations is treated using electron-phonon coupling theory. Starting from the basic principles of formal scattering theory, the elastic and inelastic scattering intensities are developed in a manner that identifies the small overlap region in the surface electron density where the projectile atom is repelled. The effective vibrational displacements of the electron gas, which lead to energy transfer through excitation of phonons, are directly related to the vibrational displacements of the atomic cores in the target crystal via electron-phonon coupling. The effective Debye-Waller factor for atom-surface scattering is developed and related to the mean square displacements of the atomic cores. The complex dependence of the Debye-Waller factor on momentum and energy of the projectile, including the effects of the attractive adsorption well in the interaction potential, are clearly defined. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known electron-phonon coupling constant lambda. This treatment reproduces the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the mode specific mass correction components lambda(Q,nu) defined by the relationship lambda = & LANGBRAC;lambda(Q,nu)& RANGBRAC;. The intensities of elastic diffraction peaks are shown to be a weighted sum over the lambda(Q,nu), and the Debye-Waller factor can also be expressed in terms of a similar weighted summation. In the simplest case the Debye-Waller exponent is shown to be proportional to lambda and for simple metals, metal overlayers, and other kinds of conducting surfaces values of lambda are extracted from available experimental data. This dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the electron-phonon coupling constant lambda shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density. (c) 2022 Elsevier B.V. All rights reserved.

The change in bending rigidity with temperature κ(T) for 2D materials is highly debated: theoretical works predict both increase and decrease. Here we present measurements of κ(T), for a 2D material: AB-stacked bilayer graphene. We obtain κ(T) from phonon dispersion curves measured with helium atom scattering in the temperature range 320-400 K. We find that the bending rigidity increases with temperature. Assuming a linear dependence over the measured temperature region we obtain κ(T)=[(1.3±0.1)+(0.006±0.001)T/K]  eV by fitting the data. We discuss this result in the context of existing predictions and room temperature measurements.

This Festschrift issue for Peter Toennies includes a collection of articles on new horizons in the dynamics of molecules: from gases to surfaces.

This corrects the article DOI: 10.1103/PhysRevLett.120.226101.

Recent theory has demonstrated that the value of the electron-phonon coupling strength λ can be extracted directly from the thermal attenuation (Debye-Waller factor) of helium atom scattering reflectivity. This theory is here extended to multivalley semimetal systems and applied to the case of graphene on different metal substrates and graphite. It is shown that λ rapidly increases for decreasing graphene-substrate binding strength. Two different calculational models are considered which produce qualitatively similar results for the dependence of λ on binding strength. These models predict, respectively, values of λHAS = 0.89 and 0.32 for a hypothetical flat free-standing single-layer graphene with cyclic boundary conditions. The method is suitable for analysis and characterization of not only the graphene overlayers considered here, but also other layered systems such as twisted graphene bilayers.