  Carbon nanotubes continue to be model systems for studies of confinement and
interactions. This is particularly true in the case of so-called "ultra-clean"
carbon nanotube devices offering the study of quantum dots with extremely low
disorder. The quality of such systems, however, has increasingly revealed
glaring discrepancies between experiment and theory. Here we address the
outstanding anomaly of exceptionally large orbital magnetic moments in carbon
nanotube quantum dots. We perform low temperature magneto-transport
measurements of the orbital magnetic moment and find it is up to seven times
larger than expected from the conventional semiclassical model. Moreover, the
magnitude of the magnetic moment monotonically drops with the addition of each
electron to the quantum dot directly contradicting the widely accepted shell
filling picture of single-particle levels. We carry out quasiparticle
calculations, both from first principles and within the effective-mass
approximation, and find the giant magnetic moments can only be captured by
considering a self-energy correction to the electronic band structure due to
electron-electron interactions.
