Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium.
J Phys Condens Matter. 2011 Jul 13;23(27):275801. doi: 10.1088/0953-8984/23/27/275801. Epub 2011 Jun 17.
We investigate the dynamics of a charged particle moving in a graphene layer and in a two-dimensional electron gas, where it obeys the Dirac and the Schrödinger equations, respectively. The charge carriers are described as Gaussian wavepackets. The dynamics of the wavepackets is studied numerically by solving both quantum-mechanical and relativistic equations of motion. The scattering of such wavepackets by step-like magnetic and potential barriers is analysed for different values of wavepacket energy and width. We find: (1) that the average position of the wavepacket does not coincide with the classical trajectory, and (2) that, for slanted incidence, the path of the centre of mass of the wavepacket does not have to penetrate the barrier during the scattering process. Trembling motion of the charged particle in graphene is observed in the absence of an external magnetic field and can be enhanced by a substrate-induced mass term.
我们研究了在石墨烯层和二维电子气中运动的带电粒子的动力学，其中它分别遵循狄拉克和薛定谔方程。电荷载流子被描述为高斯波包。通过求解量子力学和相对论运动方程，对波包的动力学进行了数值研究。分析了不同波包能量和宽度下，此类波包通过阶跃式磁场和势垒的散射。我们发现：（1）波包的平均位置与经典轨迹不重合，以及（2）对于倾斜入射，在散射过程中，波包质心的路径不一定穿透势垒。在没有外磁场的情况下，观察到了石墨烯中带电粒子的颤抖运动，并且可以通过衬底诱导的质量项来增强。
