We study the two-electron eigenspectrum of a carbon-nanotube double quantum
dot with spin-orbit coupling. Exact calculation are combined with a simple
model to provide an intuitive and accurate description of single-particle and
interaction effects. For symmetric dots and weak magnetic fields, the
two-electron ground state is antisymmetric in the spin-valley degree of freedom
and is not a pure spin-singlet state. When double occupation of one dot is
favored by increasing the detuning between the dots, the Coulomb interaction
causes strong correlation effects realized by higher orbital-level mixing.
Changes in the double-dot configuration affect the relative strength of the
electron-electron interactions and can lead to different ground state
transitions. In particular, they can favor a ferromagnetic ground state both in
spin and valley degrees of freedom. The strong suppression of the energy gap
can cause the disappearance of the Pauli blockade in transport experiments and
thereby can also limit the stability of spin-qubits in quantum information
proposals. Our analysis is generalized to an array of coupled dots which is
expected to exhibit rich many-body behavior.Comment: 14 pages, 11 pages and 1 table. Typos in text and Figs.4 and 6
correcte
