Floquet theory for the electronic stopping of projectiles in solids

The problem of electronic stopping is traditionally approached and understood in the context of linear response theory[1], or a full non-linear theory for jellium[2]. First-principles quantitative simulations using time dependent density functional theory show reasonably predictive accuracy but remain computationally expensive and do not provide a clear, intuitive understanding of the stopping processes.
We propose here a general (single-particle) stationary theory for the electronic excitation in crystalline solids by a constant-velocity projectile. It is based on the Floquet formalism for time-periodic systems[3], exploiting the system discrete translational space-time invariance. A change to the projectile’s reference frame allows for a generalization of the treatment in Ref. [2], permitting a full study of the stopping in strong coupling for any crystalline system. Non-trivial effects such as the low-velocity threshold effect can be analyzed and understood in this framework.

[1]TJ Lindhard et al.Selsk. Mat. Fys. Medd. 34 No. 4 (1964).
[2]P.M. Echenique et al., Phys. Rev. A 33, 897 (1986).
[3]J.H. Shirley, Phys. Rev. 138.4B, B979 (1965).