  The combination of strong spin orbit coupling and strong correlations holds
tremendous potential for interesting physical phenomena as well as applications
in spintronics and quantum computation. In this context, we here study the
interplay between the Rashba spin-orbit coupling (RSOC) and the Kondo screening
in noncentrosymmetric $f$-electron materials. We show that the Kondo coupling
of the $f$-electrons becomes anisotropic at high temperatures due to the RSOC.
However, an isotropic Kondo effect is restored at low temperature which leads
to a complete Kondo screening. We furthermore demonstrate that the Kondo effect
has influence on the Rashba splitting in the band structure, which becomes
temperature dependent. Although the $f$-electrons are localized at high
temperature, a helical spin polarization of the conduction band emerges due to
the scattering with the $f$-electrons. With decreasing temperature, the Kondo
screening occurs, which leads to drastic changes in the band structure.
Remarkably, these changes in the band structure depend on the helical spin
polarization. For strong RSOC, we observe that the hybridization gap of one of
the helical bands is closed at low temperature and a helical half-metal is
formed.
