Quantum Transport in Graphene near the Dirac Point

石墨烯是一种单层石墨，是一种新发现的具有显著电子性能的材料。石墨烯中的载流子用相对论狄拉克方程来描述，而不是用其他二维电子气的薛定谔方程来描述。石墨烯和迄今已知的二维电子系统之间的差异在“狄拉克点”最为明显，此时费米能量与狄拉克方程中的零能点重合。这一建议解决了狄拉克点附近输运的三个方面：依赖于时间的输运和对未掺杂石墨烯薄片中的门定义量子点的半经典理论的发展，在量化磁场中石墨烯p-n结处的共传播边态的混合，包括能量依赖和相互作用效应，以及狄拉克点附近无序石墨烯的单参数标度，其中无无序的电导率有限但很小，sigma=4e^2/pi h。门定义的量子点自然连接到``电子/空穴坑‘，在强无规势的存在下，它们在石墨烯的狄拉克点处形成，在这种情况下，决定了石墨烯的导电性。

Graphene, a single layer of graphite, is a newly discovered material with remarkable electronic properties. Charge carriers in graphene are described by the relativistic Dirac equation, instead of the Schroedinger equation that is used for other two-dimensional electron gases. Differences between graphene and hitherto known two-dimensional electron systems are most pronounced at the "Dirac point'', when the Fermi energy coincides with the zero energy point in the Dirac equation. This proposal addresses three aspects of transport near the Dirac point: Time-dependent transport and the development of a semiclassical theory for gate-defined quantum dots in an otherwise undoped graphene sheet, mixing of co-propagating edge states at a graphene p-n junction in a quantizing magnetic field, including energy dependence and interaction effects, and one-parameter scaling for disordered graphene in the vicinity of the Dirac point, where the conductivity without disorder is finite but small, sigma = 4 e^2/pi h. The gate-defined quantum dots are naturally connected to the ``electron/hole puddles'', which form in graphene at the Dirac point in the presence of a strong random potential and, in that case, determine the conductivity of graphene.