On the Kondo effect in carbon nanotubes at half halfing

Details On the Kondo effect in carbon nanotubes at half halfing On the Kondo effect in carbon nanotubes at half halfing

2004-07-08

arxiv.org/abs/cond-mat/0407193v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

full paper including figures at: http://www.unibas.ch/phys-meso/Research/Papers/2004/Kondo-4shell-SWNT.pdf

Scientific paper

10.1103/PhysRevB.70.235419

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 four-fold 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 non-linear transport measurement in this regime, in which the four-fold 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 d of the levels from perfect degeneracy and the exchange energy J. While d ~ 0.1 - 0.2 (in units of level spacing) is in agreement with previous work, the exchange term is found to be surprisingly small: J < 0.02. 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.

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