We propose a photonic structure stacked sequentially by one-dimensional photonic crystals and cavities. The whole structure is composed of single-negative and double-negative materials. The optical Wannier-Stark ladder （WSL） can be obtained in a low frequency region by modulating the widths of the cavities in order. We simulate the dynamical behavior of the electromagnetic wave passing through the proposed photonic structure. Due to the dispersive characteristics of the metamaterials, a very narrow WSL can be obtained. The long-period electromagnetic Bloch oscillation is demonstrated theoretically to have a period on a microsecond time scale.
To identify the relation between torque and superlubric motion, we investigate the interlayer sliding behavior of two graphene disks with numerical computation methods. The potential energy, lateral force and torque between the top and bottom graphene disks, which are associated with misfit angle, translational displacement and interlayer distance, are analyzed. The results show that the rotation of the top disk is feeble for commensurate state, but it is difficult to realize superlubricity due to the lateral force fluctuating remarkably. For incommensurate state, the flake exhibits vanishing torque approaching to zero only for partial sliding directions. The superlubricity between the top and bottom disks will be eliminated due to torque-induced reorientation along other sliding directions. Whether for commensurate or incommensurate contact, the amplitudes of the lateral force （516 pN and 13 pN, respectively） are in qualitative agreement with experimental observation （typically 250 pN and 50 pN, respectively）. It shows that the interlayer torque is insensitive to the top disk size with incommensurate contact. The results suggest that the superlubric motion of graphene disk can be controlled by adjusting the torque.
