Model for two-channel Kondo effect in carbon nanotube quantum dots

Abstract

The overscreened Kondo effect is shown to be feasible in a carbon nanotube quantum dot junction hosting a spin-$\frac{1}{2}$ atom with a single $s$-wave valence electron (e.g., Au). The idea is to use the two valleys $\ensuremath{\xi}=\mathbf{K},{\mathbf{K}}^{\ensuremath{'}}$ (located on two inequivalent corners of the first Brillouin zone) as two symmetry protected flavor quantum numbers. Exchange interaction between the itinerant electrons and the host atom is computed and shown to be antiferromagnetic, and it does not couple different flavors. Perturbative renormalization group analysis exposes a finite weak-coupling two-channel fixed point, where the Kondo temperature is estimated to be around $0.5--5$ K. Remarkably, occurrence of two different scaling regimes implies a nonmonotonic dependence of the conductance as a function of temperature. Consequently, in this system (unlike the ``standard'' two-channel Kondo effect), the physics of the overscreened Kondo effect is exposed already in the weak coupling regime.