Impurity scattering in carbon nanotubes - Absence of back scattering

The effective potential of an impurity in a k.p scheme is derived in two-dimensional graphite sheet. When the potential range is smaller than the lattice constant, it has an off-diagonal matrix element between K and K' points comparable to the diagonal element. With the increase of the range, this off-diagonal element decreases rapidly and the diagonal element for envelopes at A and B sites becomes identical. The crossover between these two regimes occurs around the range smaller than the lattice constant. In the latter regime, back scattering between states with +k and -k vanishes identically for the hands crossing the Fermi level in the absence of a magnetic field, leading to an extremely large conductivity The absence of the back scattering disappears in magnetic fields, giving rise to a huge positive magnetoresistance.