Ab initio electronic stationary states for nuclear projectiles in solids

Abstract

The process by which a nuclear projectile is decelerated by the electrons of the condensed matter it traverses is currently being studied by following the explicit dynamics of projectile and electrons from first principles in a simulation box with a sample of the host matter in periodic boundary conditions. The approach has been quite successful for diverse systems even in the strong-coupling regime of maximal dissipation around the Bragg peak, in spite of the nanometric finite sizes employed. This technique is here revisited for periodic solids in the light of a recently proposed Floquet theory of stopping, a time-periodic scattering framework characterising the stationary dynamical solutions for a constant velocity projectile in an infinite solid. The electronic energy uptake induced by constant-velocity protons in diamond with a system size of a thousand atoms is studied under that light, using time-dependent density-functional theory in real time. The three time regimes arising are identified, namely, the initial transient, stationary scattering, and the onset towards saturation. The stationary scattering regime is characterised by time-periodic time derivatives of both energy and excitation spectra, for which system-size convergence is needed, since the regime is established while projectile replicas do not interfere with each other significantly. Three different approaches to the calculation of the electronic stopping power are compared and discussed in the context of the various approximations involved, as well as how to understand the Floquet quasi-energy conservation of the Kohn-Sham scattering problem in the projectile's reference frame, in the context of known dissipative descriptions.