This manuscript is the result of a joint experimental and theoretical effort. We demonstrate that there is a fundamental difference between cotunneling and the Kondo effect - a distinction that has been debated repeatedly in the past. In carbon nanotubes, the two graphene-derived Dirac points can lead to a two-fold valley degeneracy in addition to spin degeneracy; each orbital "shell" of a confined electronic system can be filled with four electrons. In most nanotubes, these degeneracies are broken by the spin-orbit interaction (due to the wall curvature) and by valley mixing (due to, as recently demonstrated, scattering at the nanotube boundaries). Using an externally applied magnetic field, the quantum states involved in equilibrium (i.e., elastic, zero-bias) and nonequilibrium (i.e., inelastic, finite bias) transitions can be identified. We show theoretically and experimentally that in the case of Kondo correlations, not all quantum state pairs contribute to Kondo-enhanced transport; some of these are forbidden by symmetries stemming from the carbon nanotube single particle Hamiltonian. This is distinctly different from the case of inelastic cotunneling (at higher temperatures and/or weaker quantum dot-lead coupling), where all transitions have been observed in the past.
"Broken SU(4) symmetry in a Kondo-correlated carbon nanotube"
D. R. Schmid, S. Smirnov, M. Marganska, A. Dirnaichner, P. L. Stiller, M. Grifoni, A. K. Hüttel, and Ch. Strunk
Phys. Rev. B 91, 155435 (2015) (PDF)
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