Conductance Quantization of Massless Dirac Fermions and the Synthesis, Characterization, and Manipulation of Graphene
Graphene, a two-dimensional carbon allotrope, has interesting electronic properties resulting from its unique hexagonal mono-atomic lattice. Electronic quasiparticles in graphene, called massless Dirac fermions, are described by the Weyl equation in which the effective speed of light is the Fermi velocity, approximately c/300. Thus graphene provides a solid state system in which to study the physics of high-energy electrons or neutrinos, including interesting relativistic quantum phenomena such as Zitterbewugung, atomic collapse, and Klein tunneling. The comparison of graphene's quasiparticles to neutrinos is limited by the fact that scattering in the solid reduces the mean free path to about a micron. However, by fabricating clean graphene devices with closely spaced electrodes, one can probe the intrinsic properties of massless Dirac fermions in the ballistic regime where these quasiparticles do not undergo scattering.
The theory of the Dirac equation, the band structure of graphene, and the Landauer formalism for electronic transport is explained. Techniques are presented for the extraction of graphene, synthesis of chemical-vapor deposited graphene, and fabrication of graphene devices for both characterization and electronic transport measurements. The various characterization methods include Raman spectroscopy, atomic force microscopy, and transmission electron microscopy. Experiments approaching the ballistic transport limit in graphene devices such as point contacts, Josephson junctions, and short-and-wide junctions are described.