SU(12) Kondo effect in a carbon nanotube quantum dot

Abstract

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 ($m=0$) coalesce at the two valley points $\mathbf{K}$ and ${\mathbf{K}}^{\ensuremath{'}}$ of the first Brillouin zone and (2) the energy spectrum of electrons with $m\ensuremath{\ne}0$ 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) twofold spin degeneracy; (2) twofold isospin (valley) degeneracy; and (3) threefold orbital degeneracy $m=0,\ifmmode\pm\else\textpm\fi{}1$. 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 (with respect to the tube axis) display anisotropy with a universal ratio ${\ensuremath{\chi}}_{\mathrm{imp}}^{\ensuremath{\parallel}}/{\ensuremath{\chi}}_{\mathrm{imp}}^{\ensuremath{\perp}}=\ensuremath{\eta}$ that depends only on the electron's orbital and spin $g$ factors.