Evolution of SU(4) transport regimes in carbon nanotube Quantum Dots

Carbon nanotubes present an ideal system for investigating electronic transport at the nanoscale. In this paper, we study the evolution of conductance regimes through nanotube Quantum Dot by controlling the contact transparency in high quality samples with doubly degenerate orbitals ("shells"). For sufficiently open contacts, Kondo behavior is observed for one, two, and three electrons in the topmost shell. As the contacts are opened even more, the sample enters the "Mixed Valence" regime, where different charge states are hybridized by electron tunneling. Here, the lowtemperature conductance as a function of gate voltage shows pronounced modulations with a period of four electrons. The hallmark of the new regime is the lack of single-electron features at low temperature, which are uncovered when the temperature is raised. Finally, we find that for one and three electrons occupying a shell the zero-bias features behave distinctly differently in magnetic field.