  Ferromagnetic contacts put in proximity with carbon nanotubes induce spin and
orbital polarizations. These polarizations affect dramatically the Kondo
correlations occurring in quantum dots formed in a carbon nanotube, inducing
effective fields in both spin and orbital sectors. As a consequence, the carbon
nanotube quantum dot spectral density shows a four-fold split SU(4) Kondo
resonance. Furthermore, the presence of spin-orbit interactions leads to the
occurrence of an additional polarization among time-reversal electronic states
(polarization in the time-reversal symmetry or Kramers sector). Here, we
estimate the magnitude for the Kramer polarization in realistic carbon nanotube
samples and find that its contribution is comparable to the spin and orbital
polarizations. The Kramers polarization generates a new type of effective field
that affects only the time-reversal electronic states. We report new splittings
of the Kondo resonance in the dot spectral density which can be understood only
if Kramers polarization is taken into account. Importantly, we predict that the
existence of Kramers polarization can be experimentally detected by performing
nonlinear differential conductance measurements. We also find that, due to the
high symmetry required to build SU(4) Kondo correlations, its restoration by
applying an external field is not possible in contrast to the compensated SU(2)
Kondo state observed in conventional quantum dots.
