Graphene nanoelectromechanical systems as valleytronic devices

We investigate electronic transport in graphene nanoelectromechanical systems, known also as graphene nanodrums or nanomembranes. We demonstrate that these devices, despite their small values of strain between $0.1%$ and $1%$, can be used as efficient and robust valley polarizers and filters. Their working principle is based on the pseudomagnetic field generated by the strain of the graphene membrane. They work for ballistic electron beams as well as for strongly dispersed ones and can be also used as electron beam collimators due to the focusing effect of the pseudomagnetic field. We show additionally that the current flow can be estimated by semiclassical trajectories which represent a computationally efficient tool for predicting the functionality of the devices.