On stationary solutions for the electronic stopping of projectiles in solids

The recent proposal of a Floquet theory of electronic stopping along periodic directions in crystalline solids indicates the existence of stationary solutions for the electronic stopping problem. Some properties are predicted to be time periodic (or stroboscopically constant, as the electronic stopping power itself), while other have time-periodic time derivatives (spectral decompositions). Taking advantage of large-cell real-time time-dependent density-functional theory simulations, we explore such properties in the electronic stopping of protons in large supercells of diamond and compare them to metal hosts. We explore the velocity and direction dependence of electronic stopping power in this crystal.