Role of quantum vortices in atomic scattering from single adsorbates

Adsorbates or other defects greatly affect the physics and chemistry of surfaces. They cause, for example, scattering intensity peaks in between Bragg angles, giving rise to diffusive scattering. This phenomenon is characterized by an incoherence among particles scattered from different defects, and is well illustrated by He scattering from CO molecules adsorbed on the Pt~111! surface, for which there is a wealth of experimental data and theoretical work. Lahee et al. reported for the first time large-angle diffraction oscillations, explaining them in terms of the so-called reflection symmetry interference. This mechanism arises from the combination of adsorbate/surface double collisions, and direct scattering with the adsorbate. However, this interpretation, based on a hard-wall model, does not account for rainbow effects, which appear when realistic potentials are considered. Despite exhaustive work, some controversy regarding the assignment of the dynamical origin of diffraction peaks has been unavoidable. Arguments based on classical trajectories are not conclusive by their own nature. On the other hand, those based on pure quantum calculations lack intuitive insight. Here we show by means of Bohmian mechanics that the dynamics of this process is strongly driven by transient quantum vortices. Bohmian mechanics combines both the accuracy of the standard quantum description and an intuitive vision derived from a trajectory formalism, thus constituting a powerful tool to understand the physics underlying microscopic phenomena. In our case, a priori we may expect regular dynamics for trajectories colliding with the clean Pt surface. In a hydrodynamical view, this corresponds to a laminar regime. In contrast, the presence of the adsorbate will induce a more turbulent dynamics, leading to the formation of vortices that will play a key role. The theory of quantum vortices was first described by Dirac in a classic paper, and it has been shown that the quantization condition leading to their formation can be applied, in general, to many quantum phenomena, ranging from microscopic to macroscopic scales. In particular, here we show the important role that these vortices play in surface science, just as they do in other contexts, as superconductivity, Bose-Einstein condensation, or the Aharonov-Bohm effect. The Bohmian formalism has been recently applied suc-