Direct-space-self-consistent-phonon treatment of monolayer structures and dynamics

Computations, which would have been intractable just a few years ago, are now possible on desktop workstations. Such is the case for the application of the Self-Consistent-Phonon (SCP) approximation to large monolayer clusters on structured surfaces, combining a SCP approach to the system dynamics with a random walk approach to finding the optimum positions of the adsorbed atoms. This combination of techniques enables the investigation of the stability, structure, and dynamics of incommensurate adsorbed monolayers at low temperatures. We refer to this approach as the Direct-Space-Self-Consistent-Phonon framework. We present the application of this framework to the study of rare-gas and molecular hydrogen adsorbates on the graphite basal-plane surface and (for xenon) the Pt(111) surface. The largest cluster size consists of 4096 particles, a system that is large enough to examine incommensurate phases without significant adverse boundary effects. The existence of "pseudo-gaps" in the phonon spectrum of nearly commensurate monolayers is demonstrated, and the implication of such "pseudo-gaps" for the determination of the location of any commensurate ↔ incommensurate phase transition is explored. The stability of striped incommensurate structures vs hexagonal incommensurate structures is examined. The inherent difficulties of using this approach for the highly quantum monolayer solids is shown to generate some particular problems. Nevertheless, we demonstrate that this approach to the stability, structure, and dynamics of quantum monolayer solids is a very useful tool in the theorist's arsenal. By implication, this approach should also be useful in the study of adsorption on graphene and carbon nanotubes at low temperatures.