Centre for Applied Research in Electronics, Indian Institute of Technology Delhi, New Delhi-110016, India.
J Phys Condens Matter. 2012 May 2;24(17):175003. doi: 10.1088/0953-8984/24/17/175003. Epub 2012 Apr 5.
Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schrödinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.
单层石墨烯中的无质量狄拉克费米子在垂直入射到标量势垒时表现出完全透射，这是 O·克莱因（O Klein）最初为满足 3+1 维狄拉克方程的相对论电子预测的克莱因佯谬的结果。对于双层石墨烯，载流子是具有质量的狄拉克费米子，由于手性不同，电子和空穴态彼此不耦合。因此，入射粒子的波函数在势垒内部像非相对论薛定谔方程一样衰减。这导致在垂直入射时的透射率非常小。我们表明，在存在磁场势垒的情况下，即使在垂直入射时，这些具有质量的狄拉克费米子也可以具有透射。对于由无质量模式和具有质量模式组成的多层石墨烯，提到了这种行为的一般后果。我们还简要讨论了偏置电压对此类磁输运的影响。
