  Hyperfine interaction (HFI) in carbon nanotube and graphene quantum dots is
due to the presence of 13C atoms. We theoretically show that in these
structures the short-range nature of the HFI gives rise to a coupling between
the valley degree of freedom of the electron and the nuclear spin, in addition
to the usual electron spin-nuclear spin coupling. We predict that this property
of the HFI affects the Pauli blockade transport in carbon-based double quantum
dots. In particular, we show that transport is blocked only if both the spin
and the valley degeneracies of the quantum dot levels are lifted, e.g., by an
appropriately oriented magnetic field. The blockade is caused by four
"supertriplet" states in the (1,1) charge configuration.
