Transport gap in vertical devices made of incommensurately misoriented graphene layers

By means of atomistic tight-binding calculations, we investigate the transport properties of vertical devices made of two incommensurately misoriented graphene layers. With a chosen transport direction (Ox-axis), we define two classes of rotated graphene lattice distinguished by the different properties of their lattice symmetry and, hence, Brillouin zone, i.e., the two Dirac cones are located either at the same $k_y$-point ($K_y^{\mathrm{\prime }}=K_y=0$) or at different $k_y$-points ($K_y^{\mathrm{\prime }}=-K_y=2\pi \mathrm{/}3L_y$, where $L_y$ is the periodic length along the Oy axis). As a consequence, a misalignment of Dirac cones of two layers occurs and a significant energy-gap ($\sim$ a few hundreds of meV) of transmission is achieved in devices made of two layers of different lattice classes. We also shown that strain engineering can be used to strongly enlarge the gap in this type of device.