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We report on cotunneling spectroscopy magnetoconductance measurements ofmulti-hole ultraclean carbon nanotube quantum dots in the SU(4) Kondo regimewith strong spin-orbit coupling. Successive shells show a gradual weakening ofthe Kondo effect with respect to the spin-orbital splittings, leading to anevolution from SU(4) to SU(2) symmetry with a suppressed conductance at halfshell filling. The extracted energy level spectrum, overally consistent withnegligible disorder in the nanotube, shows in the half filled case largerenormalizations due to Coulombian effects.

Interplay of Kondo effect and strong spin-orbit coupling in multi-hole ultraclean carbon nanotubes