Impact of discrete symmetries on the Kondo effect in carbon nanotubes

Understanding the interplay between many-body correlations and non-equilibrium in systems with entangled spin and orbital degrees of freedom is central for many applications in nano-electronics. Here we demonstrate that hitherto unobserved many-body selection rules govern the Kondo effect in carbon nanotubes where spin and orbital degeneracy is broken by curvature induced spin-orbit coupling and valley mixing. They are dictated by the underlying discrete symmetries of the carbon nanotube spectrum at zero and finite magnetic field. Our measurements on a clean carbon nanotube are complemented by calculations based on a new approach to the non-equilibrium Kondo problem which reproduces the rich experimental observations in Kondo transport in high detail. Our findings open a new route to manipulate transitions between spin-orbital entangled states.