Compensation effect in carbon nanotube quantum dots coupled to polarized electrodes in the presence of spin-orbit coupling

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.