Calculation of electronic properties of multilayer graphene with Monte Carlo method and optical properties of graphene

In this thesis the electronic transport properties of bilayer graphene is investigated by Monte Carlo method and these properties are compared with monolayer graphene whenever possible. In addition the optical absorption properties of monolayer graphene is also investigated. The bilayer graphene has a quadratic energy dependence on wave vector near the points known as Dirac points in the reciprocal lattice. After a general review of monolayer graphene, bilayer graphene is investigated in detail. Scattering rates due to various mechanisms are calculated by a combination of analytical and numerical methods. For bilayer graphene the scatterings due to acoustic and optic phonon and impurities are taken into account. The chemical potential in bilayer graphene is independent of temperature and is equal to the Fermi energy of the system. The polarization function has a mild discontinuity at $k=2k_F$ at low temperatures and disappears as the temperature increases. The electronic properties of bilayer graphene is investigated by an ensemble Monte Carlo method. Velocity-time and steady state velocity-applied field curves are obtained and from the slope of velocity-field curves at low fields, the low field mobility of bilayer graphene is obtained. The dependence of mobility of bilayer graphene on temperature, electron concentration, impurity concentration, acoustic and optic deformation constants and on the dielectric constant of substrate of graphene is investigated and the mobility is observed to decrease as the temperature increases.