Electron transport in graphene

Graphene became the first and is the most vivid representative of a new class of materials. Graphene has opened a new scientific paradigm that can be studied under ordinary laboratory conditions. Graphene is a two-dimensional semiconductor with a zero-width band gap. Quasi-particles in graphene are formally described by Dirac-type Hamiltonian. The observation of the relativistic analog of the integral quantum Hall effect is the most impressive manifestation. The linear dispersion law is the most important of quantum transport that follows from the Dirac equation. Current carrying states at positive energies are similar to electrons and are negatively charged. The linear spectrum in graphene and the high value of the Fermi velocity result in enormous orbital splitting. Chirality is directly related to the relativistic nature of particles and corresponding to the linear dispersion law for massless particles.