Kondo Effects in Carbon Nanotubes: From SU(4) to SU(2) symmetry

TL;DR

This paper investigates how the Kondo effect in carbon nanotube quantum dots transitions from SU(4) to SU(2) symmetry depending on orbital mixing and asymmetry, using multiple theoretical approaches to guide experimental observation.

Contribution

It provides a detailed analysis of the role of orbital mixing and asymmetry in the emergence of different Kondo symmetries in nanotube quantum dots, with practical experimental implications.

Findings

SU(4) Kondo effect is observable under conditions of conserved orbital quantum number.

Orbital mixing and asymmetry can induce a transition from SU(4) to SU(2) Kondo symmetry.

Experimental conditions for observing pure SU(4) Kondo physics are identified.

Abstract

We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube. The K-K' double orbital degeneracy of a nanotube, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudo-spin. Screening of this pseudo-spin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. For such an exotic Kondo effect to arise, it is crucial that this orbital quantum number is conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may occur. Here we investigate in detail the role of mixing and asymmetry in the tunneling coupling and analyze how different Kondo effects, from the SU(4) symmetry to a two-level SU(2) symmetry, emerge depending on the mixing and/or asymmetry. We use four different theoretical approaches to address both the linear and non-linear conductance for different values of the external magnetic field. Our results point out clearly the experimental conditions to observe exclusively SU(4) Kondo physics. Although we focus on nanotube quantum dots, our results also apply to vertical quantum dots. We also mention that a finite amount of orbital mixing corresponds, in the pseudospin language, to having non-collinear leads with respect to the orbital ''magnetization'' axis which defines the two pseudospin orientations in the nanotube quantum dot. In this sense, some of our results are also relevant to the problem of a Kondo quantum dot coupled to non-collinear ferromagnetic leads.