  We investigate the influence of spin-orbit coupling on the Kondo effects in
carbon nanotube quantum dots, using the numerical renormalization group
technique. A sufficiently large spin-orbit coupling is shown to destroy the
SU(4) Kondo effects at zero magnetic field, leaving only two SU(2) Kondo
effects in the one- and three-electron Coulomb blockade valleys. On applying a
finite magnetic field, two additional, spin-orbit induced SU(2) Kondo effects
arise in the three- and two-electron valleys. Using physically realistic model
parameters, we calculate the differential conductance over a range of gate
voltages, temperatures and fields. The results agree well with measurements
from two different experimental devices in the literature, and explain a number
of observations that are not described within the standard framework of the
SU(4) Anderson impurity model.
