Nondiagonal Graphene Conductivity in the Presence of In-Plane Magnetic Fields

We study the electron/hole transport in puddle-disordered and rough graphene samples which are subject to in-plane magnetic fields. Previous treatments, mostly devoted to regimes where the electron/hole scattering wavelengths are larger than the surface height correlation length, are based on the use of transport equations with appropriate forms for the collision term. We point out in this work, as a counterpoint, that classical Lorentz force effects, which are expected to hold when the Fermi level is far enough away from the charge neutral point, can be heuristically assessed through disordered Boltzmann equations that contain magnetic-field dependent material derivatives, and keep the zero magnetic-field structure of the collision term. It turns out that the electric conductivity tensor gets a peculiar nondiagonal component, induced by the in-plane magnetic field that crosses the rough topography of the graphene sheet, even if the projected random transverse magnetic field vanishes in the mean. Numerical estimates of the transverse conductivities suggest that they are suitable of observation under conditions which are within the reach of up-to-date experimental methods.