SU(12) Kondo Effect in Carbon Nanotube Quantum Dot

We study the Kondo effect in a CNT(left lead)-CNT(QD)-CNT(right lead) structure. Here CNT is a single-wall metallic carbon nanotube, for which 1) the valence and conduction bands of electrons with zero orbital angular momentum ($m=0$) coalesc at the two valley points ${\bf{K}}$ and ${\bf{K}}'$ of the first Brillouin zone and 2) the energy spectrum of electrons with $m \ne 0$ has a gap whose size is proportional to $|m|$. Following adsorption of hydrogen atoms and application of an appropriately designed gate potential, electron energy levels in the CNT(QD) are tunable to have: 1) two-fold spin degeneracy; 2) two-fold isospin (valley) degeneracy; 3) three-fold orbital degeneracy $m=0,\pm1$. As a result, an SU(12) Kondo effect is realized with remarkably high Kondo temperature. Unlike the SU(2) case, the low temperature conductance and magnetic susceptibility have a peak at finite temperature. Moreover, the magnetic susceptibilities for parallel and perpendicular magnetic fields (WRT the tube axis) display anisotropy with a universal ratio $\chi_{\rm{imp}}^\parallel / \chi_{\rm{imp}}^\perp=\eta$ that depends only on the electron's orbital and spin $g$ factors.