Graphene multilayers in the crossed in-plane magnetic and out-of-plane electric fields

We report an experimental study of the out-of-plane differential conductivity $dI/dV$ in graphite mesas as a function of applied out-of-plane voltage $V$ in the in-plane magnetic fields $B_y$ up to 55 T. The spectrum $dI/dV$ vs $V$ has a pronounced peak at the critical voltage $V_0$, which grows linearly with the magnetic field $V_0\propto B_y$. The experimental results are consistent with a theoretical model. The electronic energy spectrum on each graphene layer is given by the two-dimensional (2D) Dirac cone $\varepsilon = v |p|$, where $v$ and $p = (p_x,p_y)$ are the velocity and 2D momentum. As a result of magnetic field $B_y$, the Dirac cones of the consecutive layers are shifted in the momentum space by $\Delta p_x = eB_yd$, where $d$ is a distance between the layers. Whereas electric field $E_z$ shifts the energy by $\Delta \varepsilon = E_z d$. For generic $E_z$ and $B_y$, the wave functions are localized on a finite number of layers in the $z$ direction. However, when the resonant condition $\Delta \varepsilon = v\Delta p_x$ is achieved, i.e. when $E_z = vB_y$, the Dirac cones align, and wave functions become delocalized in the $z$ direction. We believe that the resonant delocalization of the wave functions corresponds to the peak in differential conductance.