The magnetic ratchet effect in bilayer graphene

Experiments [1] have measured a magnetic ratchet effect for electrons in hydrogenated monolayer graphene, an effect in which a d.c. electric current is generated from an a.c. electric field in the presence of an in-plane magnetic field and spatial asymmetry. Here, we describe the theory of the magnetic ratchet effect in bilayer graphene. The Boltzmann kinetic equation [2,3] is used to relate the d.c. current to the scattering probability of electrons in bilayer graphene. Taking into account details of the low-energy band structure of bilayer graphene, including interlayer hopping parameters, we compare contributions arising from gate- and disorder-induced spatial asymmetry, illustrating that bilayer and multilayer graphenes are natural candidates for the study of non-linear transport effects. [1] C. Drexler et al, Nature Nanotechnology 8, 104 (2013). [2] V. I. Fal'ko, Sov. Phys. Solid State 31, 561 (1989). [3] S. A. Tarasenko, Phys. Rev. B 83, 035313 (2011).