Transport in graphene superimposed by a moving electrical superlattice potential

We calculate dc conductivities of ballistic graphene undulated by an overlying moving unidirectional electrical superlattice (SL) potential whose SL velocity is smaller than the electron velocity. We obtain no dependence of the conductivity on the velocity along the direction of the superlattice wave vector. In the orthogonal direction however, the dependence is strong on the velocity especially at voltages where a new Dirac point emerges for zero velocity. It is shown that the infinite graphene system can serve as an ideal motion detector at potentials where the first new Dirac point emerges. There the conductivity is zero at vanishing SL velocities and jumps to infinity when the SL starts moving. For finite systems at voltages where the number of new Dirac points is of the order of the ratio of the electron velocity by the SL velocity, the modifications to the conductivity of a moving SL is at least of similar magnitude as the conductivity of the stagnant SL.