# Research Highlights

## Electronic stopping of projectiles revisited

The authors propose a theoretical framework that allows analysing the electronic stopping of charged ions (projectiles) in crystalline systems, which constitutes the basis for future general and accurate computational methods.

When a charged projectile shoots through a periodic direction of the crystal,
a change of reference frame to the projectile provides time periodicity:
the figure shows the evolution of crystalline plus projectile potential (potential vs x)
in (top) the laboratory reference frame
and in (bottom) the projectile.
*a* is the lattice parameter, the period *τ = a/v*,
and *v* is the projectile velocity.
Thicker lines indicate times separated by a period.

Particles shooting through matter slow down when interacting with nuclei and electrons
via *stopping processes*.
The study of such processes is of applied interest in various contexts: the effect of radiation
in matter is important in nuclear and aerospace industries and for medical applications.
From the fundamental side, it represents a quite canonical problem in the field of strongly
nonequilibrium electronic systems.
In an article published in Physical Review Research, the authors show that it is possible
to analyse the electronic stopping of projectiles in crystals using Floquet theory for
time-periodic Hamiltonians, which is the time analogous of Bloch theorem for electrons
in crystals (see accompanying figure). The theory does not rely on the most widely used
approximations for the theoretical modelling of stopping processes:
1. Perturbative or linear-response, assuming weak interactions between the projectile
and the host material; 2. Jellium, with the electron system modelled as a homogeneous electron liquid.
Going beyond such approximations is essential: in stopping processes the projectile-target
interaction is often strong, and the use of models based on jellium cannot accurately calculate
the behaviour of semiconductors and insulators, which are of fundamental importance for applications.
Indeed, the use of Floquet theory allows the authors to analyse and characterise a
nontrivial effect in insulators, experimentally observed but so far hard to fully explain
theoretically: the appearance of a *threshold velocity* for the onset of electronic stopping power.

Floquet theory for the electronic stopping of projectiles in solids
,
N. Forcellini, E. Artacho, Phys. Rev. Research **2**, 033151 (2020)