In this overview paper, we present low-temperature electronic transport measurements of carbon nanotube quantum dots with a back gate. In a semiconducting tube, charge carriers could be completely depleted. The addition energy and the excitation spectrum have been studied as a function of the number of charges (electrons or holes), one by one. We observe electron–hole symmetry, which is a direct consequence of the symmetric band structure of the nanotube. The excitation spectrum for metallic nanotubes exhibits four-fold shell filling and is completely described by an extended constant-interaction model. Furthermore, nanotubes with a four-fold shell structure are investigated in a parallel magnetic field. The magnetic field induces a large splitting between the two orbital states of each shell, demonstrating their opposite magnetic moment and determining transitions in the spin and orbital configuration of the quantum dot ground state. Also, a small coupling is found between orbitals with opposite magnetic moments leading to anti-crossing behaviour at zero field. Current–voltage characteristics of suspended carbon nanotube quantum dots show an additional series of steps equally spaced in voltage. The energy scale of this harmonic, low-energy excitation spectrum is consistent with that of the longitudinal low-k phonon mode (stretching mode) in the nanotube. Finally, we report on a fully tunable carbon nanotube double quantum dot. We perform inelastic transport spectroscopy via the excited states in the double quantum dot, a necessary step towards the implementation of new microwave-based experiments for quantum information technology. (Some figures in this article are in colour only in the electronic version) 1
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