| In carbon nanotube dots the fourfold level degeneracy with respect to the spin and valley index K, K' is lifted by intervalley coupling, resulting from disorder, the confining potential, spin-orbit interactions due to the tube curvature, or a magnetic field. Recent transport experiments confirm the single-particle level structure probed by cotunneling spectroscopy. In the basis of single-particle eigenstates of the isolated dot the inner four levels lead to pairs of strongly and weakly coupled levels in absence of magnetic field. In addition to the Kondo ridges at zero field, the crossings of levels originating from different shells give rise to Kondo ridges at finite magnetic field. The observed bending with respect to the Kondo ridges at zero field turns out be a consequence of the magnetic-field dependence of the level-reservoir coupling strengths. Theoretical understanding is provided by using the functional renormalization-group approach, which reproduces the features of the linear conductance measurements as a function of the applied gate voltage and magnetic field. In particular the bending of the Kondo ridges at finite magnetic field is traced back to the renormalization of the couplings. |
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