  Under which conditions do the electrical transport properties of
one-dimensional (1D) carbon nanotubes (CNTs) and 2D graphene become equivalent?
We have performed atomistic calculations of the phonon-limited electrical
mobility in graphene and in a wide range of CNTs of different types to address
this issue. The theoretical study is based on a tight-binding method and a
force-constant model from which all possible electron-phonon couplings are
computed. The electrical resistivity of graphene is found in very good
agreement with experiments performed at high carrier density. A common
methodology is applied to study the transition from 1D to 2D by considering
CNTs with diameter up to 16 nm. It is found that the mobility in CNTs of
increasing diameter converges to the same value, the mobility in graphene. This
convergence is much faster at high temperature and high carrier density. For
small-diameter CNTs, the mobility strongly depends on chirality, diameter, and
existence of a bandgap.
