Kondo effect in carbon nanotubes at half filling -: art. no. 235419

In a single state of a quantum dot the Kondo effect arises due to the spin-degeneracy, which is present if the dot is occupied with one electron (N=1). The eigenstates of a carbon nanotube quantum dot possess an additional orbital degeneracy leading to a fourfold shell pattern. This additional degeneracy increases the possibility for the Kondo effect to appear. We revisit the Kondo problem in metallic carbon nanotubes by linear and nonlinear transport measurement in this regime, in which the fourfold pattern is present. We have analyzed the ground state of CNTs, which were grown by chemical vapor deposition, at filling N=1, N=2, and N=3. Of particular interest is the half-filled shell, i.e., N=2. In this case, the ground state is either a paired electron state or a state for which the singlet and triplet states are effectively degenerate, allowing in the latter case for the appearance of the Kondo effect. We deduce numbers for the effective missmatch delta of the levels from perfect degeneracy and the exchange energy J. While deltasimilar to0.1-0.2 (in units of level spacing) is in agreement with previous work, the exchange term is found to be surprisingly small: Jless than or similar to0.02. In addition we report on the observation of gaps, which in one case is seen at N=3 and in another is present over an extended sequence of levels.