# Intra- and inter-shell Kondo effects in carbon nanotube quantum dots

## TL;DR

This paper investigates the complex Kondo effects in carbon nanotube quantum dots, revealing how magnetic fields and interactions induce various degeneracies and exotic many-body phenomena.

## Contribution

It introduces a finite-U mean field slave boson approach to analyze intra- and inter-shell Kondo effects, including SU(3) and SU(4) symmetries, in nanotube quantum dots.

## Key findings

- Magnetic fields can restore Kondo correlations suppressed by spin-orbit interaction.
- Exotic SU(3) and SU(4) Kondo effects can emerge due to degeneracies.
- Short-range Coulomb interactions induce effective intervalley exchange leading to threefold degeneracy.

## Abstract

The linear response transport properties of carbon nanotube quantum dot in the strongly correlated regime are discussed. The finite-U mean field slave boson approach is used to study many-body effects. Magnetic field can rebuilt Kondo correlations, which are destroyed by the effect of spin-orbit interaction or valley mixing. Apart from the field induced revivals of SU(2) Kondo effects of different types: spin, valley or spin-valley, also more exotic phenomena appear, such as SU(3) Kondo effect. Threefold degeneracy occurs due to the effective intervalley exchange induced by short-range part of Coulomb interaction or due to the intershell mixing. In narrow gap nanotubes the full spin-orbital degeneracy might be recovered in the absence of magnetic field opening the condition for a formation of SU(4) Kondo resonance.