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

TL;DR

This study explores how spin-orbit interaction and valley mixing influence the Kondo effect in carbon nanotube quantum dots, revealing a crossover from SU(4) to SU(2) symmetry and analyzing the impact of magnetic fields.

Contribution

It provides a detailed numerical analysis of the Kondo crossover induced by symmetry-breaking perturbations in CNTs, supported by scaling arguments and spectral function insights.

Findings

Kondo crossover from SU(4) to SU(2) occurs with increasing symmetry breaking.

Kondo temperature scales inversely with the spectral splitting Δ.

Magnetic fields can induce Kondo revivals under certain conditions.

Abstract

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 $\Delta$ 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 $\Delta$ 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.