Many-body entanglement is at the heart of the Kondo effect, which has itshallmark in quantum dots as a zero-bias conductance peak at low temperatures.It signals the emergence of a conducting singlet state formed by a localizeddot degree of freedom and conduction electrons. Carbon nanotubes offer thepossibility to study the emergence of the Kondo entanglement by tuningmany-body correlations with a gate voltage. Here we quantitatively show anundiscovered side of Kondo correlations, which counterintuitively tend to block conductionchannels: inelastic cotunneling lines in the magnetospectrum of a carbonnanotube strikingly disappear when tuning the gate voltage. Considering theglobal \SUT\ $\otimes $ \SUT\ symmetry of a carbon nanotube coupled to leads,we find that only resonances involving flips of the Kramers pseudospins,associated to this symmetry, are observed at temperatures and voltages belowthe corresponding Kondo scale. Our results demonstrate the robust formation ofentangled many-body states with no net pseudospin.
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