Quantum–classical simulations of the electronic stopping force and charge on slow heavy channelling ions in metals

Abstract

By simulating the passage of heavy ions along open channels in a model crystalline metal using semi-classical Ehrenfest dynamics we directly investigate the nature of non-adiabatic electronic effects. Our time-dependent tight-binding approach incorporates both an explicit quantum mechanical electronic system and an explicit representation of a set of classical ions. The coupled evolution of the ions and electrons allows us to explore phenomena that lie beyond the approximations made in classical molecular dynamics simulations and in theories of electronic stopping. We report a velocity-dependent charge-localization phenomenon not predicted by previous theoretical treatments of channelling. This charge localization can be attributed to the excitation of electrons into defect states highly localized on the channelling ion. These modes of excitation only become active when the frequency at which the channelling ion moves from interstitial point to equivalent interstitial point matches the frequency corresponding to excitations from the Fermi level into the localized states. Examining the stopping force exerted on the channelling ion by the electronic system, we find broad agreement with theories of slow ion stopping (a stopping force proportional to velocity) for a low velocity channelling ion (up to about 0.5 nm fs−1 from our calculations), and a reduction in stopping power attributable to the charge localization effect at higher velocities. By exploiting the simplicity of our electronic structure model we are able to illuminate the physics behind the excitation processes that we observe and present an intuitive picture of electronic stopping from a real-space, chemical perspective.