Transport in nanostructures and nanotubes

In two-dimensional honeycomb lattices, electronic states are described by Weylʹs equation for a massless neutrino when each site is occupied by an electron on average. The system has a topological singularity at the origin k=0 of the wave vector, giving rise to nontrivial Berryʹs phase when k is rotated around the origin. The singularity causes discrete jumps in the conductivity at the energy corresponding to k=0 in honeycomb lattices and leads to the absence of backscattering and a perfect conductance in carbon nanotubes.