The possibility to effect valley splitting of an electronic current in graphene represents the essential component in the new field of valleytronics in such two-dimensional materials. Based on a symmetry analysis of the scattering matrix, we show that if the spatial distribution of multiple potential scatterers breaks mirror symmetry about the axis of incoming electrons, then a splitting of the current between two valleys is observed. This leads to the appearance of the valley Hall effect. We illustrate the effect of mirror symmetry breaking in a minimal system of two symmetric impurities, demonstrating the splitting between valleys via the differential cross sections and non-vanishing skew parameter. We further discuss the role that these effects may play in transport experiments.
@article{arxiv.1706.04636,
title = {Minimal Geometry for Valley Filtering in Graphene},
author = {Mahmoud M. Asmar and Sergio E. Ulloa},
journal= {arXiv preprint arXiv:1706.04636},
year = {2017}
}