Magnetic fields force ballistic electrons injected from a narrow contact to move along skipping orbits and form caustics. This leads to pronounced resistance peaks at nearby voltage probes as electrons are effectively focused inside them, a phenomenon known as magnetic focusing. This can be used not only for the demonstration of ballistic transport but also to study the electronic structure of metals. Here we use magnetic focusing to probe narrow bands in graphene bilayers twisted at 2 degrees. Their minibands are found to support long-range ballistic transport limited at low temperatures by intrinsic electron-electron scattering. A voltage bias between the layers causes strong valley splitting and allows selective focusing for different valleys, which is of interest for using this degree of freedom in frequently-discussed valleytronics.
@article{arxiv.1911.02827,
title = {Minibands in twisted bilayer graphene probed by magnetic focusing},
author = {A. I. Berdyugin and B. Tsim and P. Kumaravadivel and S. G. Xu and A. Ceferino and A. Knothe and R. Krishna Kumar and T. Taniguchi and K. Watanabe and A. K. Geim and I. V. Grigorieva and V. I. Fal'ko},
journal= {arXiv preprint arXiv:1911.02827},
year = {2020}
}