This paper provides a theoretical description of sequential tunneling transport and spectroscopy, in carbon nanotube quantum dots weakly tunnel coupled to metallic leads under a voltage bias. The effects of Coulomb blockade charging, spin-orbit fine structure, and orbital- and spin-Zeeman effects arising from coupling to applied magnetic fields are considered; and the dependence of the conductance upon applied gate voltage, bias voltage, and magnetic fields is determined. The work is motivated by recent experiments on ultraclean carbon nanotube dots [Kuemmeth et al, Nature (London)452, 448 (2008)], to which comparison is made.

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Formally, this reflects the invariance of Ĥso+ĤB, under the following canonical transformation: d1σσd2σ (with σ=±, for ↑/↓, spins). By contrast, Ĥso+ĤB is not invariant.

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Additional many-body spectral broadening can, in fact, be captured approximately on replacing Γ>, in Eq. (34) by an effective N-dependent Γeff which mimics the so-called blocking effects. This would, however, be overelaboration in the context of the present work, since the resulant Γeff’s remain small compared to the typical spacing between the states of the isolated dot.

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Although readily included, addition excitations to the Ng=N+1 ground state are of order Ec=U above this ground state and, in consequence, lie well in excess of the eVsd “window” considered in the vicinity of the Ng=NN+1 border. Directly analogous comments naturally apply to removal excitations from the Ng=N ground state.

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