  Motivated by a recent experiment [F. Pei et al., Nat. Nanotech. 7, 630
(2012)], we theoretically study the Pauli blockade transport effect in a double
quantum dot embedded in a bent carbon nanotube. We establish a model for Pauli
blockade, taking into account the strong g-factor anisotropy that is linked to
the local orientation of the nanotube axis in each quantum dot. We provide a
set of conditions under which our model is approximately mapped to the
spin-blockade model of Jouravlev and Nazarov [O. N. Jouravlev and Y. V.
Nazarov, Phys. Rev. Lett. 96, 176804 (2006)]. The results we obtain for the
magnetic anisotropy of the leakage current, together with their qualitative
geometrical explanation, provide a possible interpretation of previously
unexplained experimental results. Furthermore, we find that in a certain
parameter range, the leakage current becomes highly sensitive to the shape of
the tube, and this sensitivity increases with increasing g-factor anisotropy.
This mutual dependence of the electron transport and the tube shape allows for
mechanical control of the leakage current, and for characterization of the tube
shape via measuring the leakage current.
