Surface-scattering study of the interaction potential of He atoms with the step edges of the Cu(211) and Cu(511) vicinal surfaces

Reply to the 'Comment on "Perturbation theory of scattering for grazing-incidence fast-atom diffraction"' by G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, E. M. S. Casagrande, E. A. Sánchez, M. S. Gravielle and H. Khemliche, Phys. Chem. Chem. Phys., 2023, , DOI: 10.1039/D3CP02486E

In this Reply, we show that criticisms of perturbation theory for grazing-incidence fast-atom diffraction (GIFAD) are ill-founded. We show explicitly that our formulation (W. Allison, S. Miret-Artés and E. Pollak, Phys. Chem. Chem. Phys., 2022, 24, 15851) provides a similar precision in describing the observed phenomena as ab initio potentials. Since that is the main criterion to distinguish between methods, it seems reasonable to conclude that the perturbation approach using a Morse-type potential reproduces the essential aspects of the dynamics correctly. In addition we expand on the historical context and summarize the physical insights provided by our methods.

Surface electronic corrugation of a one-dimensional topological metal: Bi(114)

The surface of Bi(114) is a striking example where the reduced dimensionality gives rise to structural rearrangement and new states at the surface. Here, we present a study of the surface structure and electronic corrugation of this quasi one-dimensional topological metal based on helium atom scattering (HAS) measurements. In contrast to low-index metal surfaces, upon scattering from the stepped (114) truncation of Bi, a large proportion of the incident beam is scattered into higher order diffraction channels which in combination with the large surface unit cell makes an analysis challenging. The surface electronic corrugation of Bi(114) is determined, using measurements upon scattering normal to the steps, together with quantum mechanical scattering calculations. Therefore, minimisation routines that vary the shape of the corrugation are employed, in order to minimise the deviation between the calculations and experimental scans. Furthermore, we illustrate that quantum mechanical scattering calculations can be used to determine the orientation of the in- and outgoing beam with respect to the stepped surface structure.

Diffraction of helium on MgO(100) surface calculated from first-principles

In this work we simulate the diffraction peak intensities of He beams scattered on the MgO(100) surface using hierarchical protocol, based on periodic and finite-cluster quantum-chemical calculations.

Helium atom scattering investigation of the Sb(111) surface

The Sb(111) surface was studied with helium atom scattering (HAS). Elastic HAS at different energies of the incident helium beam (15.3, 21.9, 28.4 meV) was applied for structural investigations. The lattice constants derived from the positions of the observed diffraction peaks up to third order were found to be in perfect agreement with previous structure determinations of Sb(111). The observed diffraction patterns with clear peaks up to second order were used to model the electronic surface corrugation with the GR method. As an estimation for the attractive part of the interaction potential a well depth of (4.0 ± 0.5) meV was found. Best fit results were obtained with a corrugation height of 12-13% of the lattice constant, which is rather large compared to other surfaces with metallic character. Intensity measurements of the specular peak as a function of incident energy were analysed to determine the distribution of terraces on the surface. The results show a quite flat Sb(111) surface and a step height of 3.81 Å of the remaining terraces.

He atom scattering from ZnO surfaces: calculation of diffraction peak intensities using the close-coupling approach

Diffraction intensities of a molecular He beam scattered off the clean and water-covered ZnO(1010) surface have been simulated using a new potential model in conjunction with the close-coupling formalism. The effective corrugation functions for the systems He-H2O/ZnO(1010) and He-H2O/ZnO(1010) have been obtained from density functional theory calculations within the Esbjerg-Nørskov approximation. Using these data a potential model is constructed consisting of a corrugated Morse potential at small He-surface distances and a semiempiric attractive part at larger distances. The diffraction patterns obtained from close-coupling calculations agree with the experimental data within about 10%, which opens the possibility to simulate He diffraction from surfaces of any structural complexity and to verify surface and adsorbate structures proposed theoretically by employing this kind of analysis.

Classical Wigner theory of gas surface scattering

The scattering of atoms from surfaces is studied within the classical Wigner formalism. A new analytical expression is derived for the angular distribution and its surface temperature dependence. The expression is valid in the limit of weak coupling between the vertical motion with respect to the surface and the horizontal motion of the atom along the periodic surface. The surface temperature dependence is obtained in the limit of weak coupling between the horizontal atomic motion and the surface phonons. The resulting expression, which takes into account the surface corrugation, leads to an almost symmetric double peaked angular distribution, with peaks at the rainbow angles. The analytic expression agrees with model numerical computations. It provides a good qualitative description for the experimentally measured angular distribution of Ne and Ar scattered from a Cu surface.

A causal look into the quantum Talbot effect

A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.

Quantum trajectories in elastic atom-surface scattering: threshold and selective adsorption resonances

The elastic resonant scattering of He atoms off the Cu(117) surface is fully described with the formalism of quantum trajectories provided by Bohmian mechanics. Within this theory of quantum motion, the concept of trapping is widely studied and discussed. Classically, atoms undergo impulsive collisions with the surface, and then the trapped motion takes place covering at least two consecutive unit cells. However, from a Bohmian viewpoint, atom trajectories can smoothly adjust to the equipotential energy surface profile in a sort of sliding motion; thus the trapping process could eventually occur within one single unit cell. In particular, both threshold and selective adsorption resonances are explained by means of this quantum trapping considering different space and time scales. Furthermore, a mapping between each region of the (initial) incoming plane wave and the different parts of the diffraction and resonance patterns can be easily established, an important issue only provided by a quantum trajectory formalism.