Few-electron physics in a nanotube quantum dot with spin-orbit coupling

We study the few-electron eigenspectrum of a nanotube quantum dot with spin-orbit coupling. The two-electron phase diagram as a function of the length of the dot and the applied parallel magnetic field shows clear signatures of both spin-orbit coupling and electron-electron interaction. Below a certain critical length, ground-state transitions are correctly predicted by a single-particle picture and are mainly independent of the length of the dot despite the presence of strong correlations. However, for longer quantum dots the critical magnetic field strongly decreases with increasing length, which is a pure interaction effect. In fact, the new ground state is spin and valley polarized, which implies a strong occupation of higher longitudinal modes.