  We study theoretically the Kondo effect in carbon nanotube quantum dot
attached to polarized electrodes. Since both spin and orbit degrees of freedom
are involved in such a system, the electrode polarization contains the spin-
and orbit-polarizations as well as the Kramers polarization in the presence of
the spin-orbit coupling. In this paper we focus on the compensation effect of
the effective fields induced by different polarizations by applying magnetic
field. The main results are i) while the effective fields induced by the spin-
and orbit-polarizations remove the degeneracy in the Kondo effect, the
effective field induced by the Kramers polarization enhances the degeneracy
through suppressing the spin-orbit coupling; ii) while the effective field
induced by the spin-polarization can not be compensated by applying magnetic
field, the effective field induced by the orbit-polarization can be
compensated; and iii) the presence of the spin-orbit coupling does not change
the compensation behavior observed in the case without the spin-orbit coupling.
These results are observable in an ultraclean carbon-nanotube quantum dot
attached to ferromagnetic contacts under a parallel applied magnetic field
along the tube axis and it would deepen our understanding on the Kondo physics
of the carbon nanotube quantum dot.
