chapter  23
14 Pages

## Graphene Quantum Dots

Graphene is a layer of crystalline carbon that just one atom thick (Novoselov et al. 2004). Graphene is a two-dimensional crystal with a honeycomb structure. ™e crystalline structure of graphene results in a very unique energy dispersion law (Wallace 1947). Namely, the low-energy excitations are described by the Dirac-Weyl equations for massless relativistic particles with a linear dependence on a momentum (Ando 2002). ™is property of graphene makes it a very interesting academic material, which has been studied theoretically in great detail for the last 50 years. But only in 2004, graphene has been realized experimentally (Novoselov et al. 2004). Since then graphene has been a subject of extensive theoretical and experimental research (Ando et al. 1998, Novoselov et al. 2005, Katsnelson 2007). Now high-quality graphene crystallites with the sizes up to 100μm can be easily grown (Novoselov et al. 2005). ™e quality of graphene crystals is very high and is suÀcient for many research and commercial applications. ™e charge carriers in graphene can travel thousands of interatomic distances without scattering. ™e mobility of the carriers is high (exceeding 15,000cm2/V s) and has weak dependence on the temperature up to 300K. Even with the doping, when the electron density exceeds 1012 cm−2, the mobility is still high. ™e manifestation of the extremely high quality of graphene is observation of the quantum Hall e£ect in this system (Zhang et al. 2005).