Electrically tunable transverse magnetic focusing in graphene

Abstract

Electrons can travel though very pure materials without scattering from defects. In this ballistic regime, magnetic fields can manipulate the electron trajectory. Such magnetic electron focusing is now observed in graphene. Although the effect has previously been seen in metals and semiconductors, it is evident in graphene at much higher temperatures—including room temperature. Electrons in a periodic lattice can propagate without scattering for macroscopic distances despite the presence of the non-uniform Coulomb potential due to the nuclei1. Such ballistic motion of electrons allows the use of a transverse magnetic field to focus electrons2. This phenomenon, known as transverse magnetic focusing (TMF), has been used to study the Fermi surface of metals3 and semiconductor heterostructures4, as well as to investigate Andreev reflection3 and spin–orbit interaction5, and to detect composite fermions6,7. Here we report on the experimental observation of TMF in high-mobility mono-, bi- and tri-layer graphene devices. The ability to tune the graphene carrier density enables us to investigate TMF continuously from the hole to the electron regime and analyse the resulting focusing fan. Moreover, by applying a transverse electric field to tri-layer graphene, we use TMF as a ballistic electron spectroscopy method to investigate controlled changes in the electronic structure of a material. Finally, we demonstrate that TMF survives in graphene up to 300 K, by far the highest temperature reported for any system, opening the door to new room-temperature applications based on electron-optics.