Crossover between quantum and classical transport: quantum Hall effect and carbon nanotubes

A crossover occurs in transport between quantum and classical regimes due to the presence of inelastic scattering. In the integer quantum Hall effect, the quantum regime corresponds to the edge-current picture and the classical to the bulk Hall current picture. The behavior of the local voltage distribution demonstrates this crossover. In a metallic carbon nanotube, there is a perfectly conducting channel independent of energy for scatterers having a potential range larger than the lattice constant. When several bands coexist at the Fermi level, the perfect channel is destroyed by inelastic scattering and therefore the resulting conductance differs completely between two regimes.