A model able to explain the complicated structure of electronic stopping at low velocities in insulating materials is presented. It is shown to be in good agreement with results obtained from time-dependent density-functional theory for the stopping of a channeling Si atom in a Si crystal. If we define the repeat frequency $f=v/\lambda$, where $\lambda$ is the periodic repeat length of the crystal along the direction the channeling atom is traveling, and $v$ is the velocity of the channeling atom, we find that electrons experience a perturbing force that varies in time at integer multiples $l$ of $f$. This enables electronic excitations at low atom velocity, but their contributions diminish rapidly with increasing values of $l$. The expressions for stopping power are derived using adiabatic perturbation theory for many-electron systems, and they are then specialized to the case of independent electrons. A simple model for the nonadiabatic matrix elements is described, along with the procedure for determining its parameters.

• Received 12 April 2016
• Revised 12 May 2016

DOI:https://doi.org/10.1103/PhysRevB.93.245106