Reprint of : Kondo effect in a carbon nanotube with spin–orbit interaction and valley mixing: A DM-NRG study

•Global symmetries of a CNT quantum dot in the Kondo regime are analyzed.•They are shown to profoundly impact various transport quantities.•We show that the Kondo temperature scales inversely with the inter-Kramers splitting.•Conditions for the occurrence of Kondo revivals in magnetic fields are discussed.

We investigate the effects of spin–orbit interaction (SOI) and valley mixing on the transport and dynamical properties of a carbon nanotube (CNT) quantum dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry in the CNT spectrum but preserve time-reversal symmetry, they induce a finite splitting ΔΔ between formerly degenerate Kramers pairs. Correspondingly, a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of these symmetry breaking parameters is varied. Clear signatures of the crossover are discussed both at the level of the spectral function as well as of the conductance. In particular, we demonstrate numerically and support with scaling arguments that the Kondo temperature scales inversely with the splitting ΔΔ in the crossover regime. In presence of a finite magnetic field, time reversal symmetry is also broken. We investigate the effects of both parallel and perpendicular fields (with respect to the tube's axis) and discuss the conditions under which Kondo revivals may be achieved.