Valley notch filter in a graphene strain superlattice: Green's function and machine learning approach

The valley transport properties of a superlattice of out-of-plane Gaussian deformations are calculated using a Green's function and a machine learning approach. Our results show that periodicity significantly improves the valley filter capabilities of a single Gaussian deformation; these manifest themselves in the conductance as a sequence by valley filter plateaus. We establish that the physical effect behind the observed valley notch filter is the coupling between counterpropagating transverse modes; the complex relationship between the design parameters of the superlattice and the valley filter effect make it difficult to estimate in advance the valley filter potentialities of a given superlattice. With this in mind, we show that a deep neural network can be trained to predict valley polarization with a precision similar to the Green's function but with much less computational effort. (AU)