We predict unusual (for non-relativistic quantum mechanics) electron states in graphene, which are localized within a finite-width potential barrier. The density of localized states in the sufficiently high and/or wide graphene barrier exhibits a number of singularities at certain values of the energy. Such singularities provide quantum oscillations of both the transport (e.g., conductivity) and thermodynamic properties of graphene - when increasing the barrier height and/or width, similarly to the well-known Shubnikov-de-Haas (SdH) oscillations of conductivity in pure metals. However, here the SdH-like oscillations are driven by an electric field instead of the usual magnetically-driven SdH-oscillations.
@article{arxiv.0712.1407,
title = {Voltage-driven quantum oscillations in graphene},
author = {V. A. Yampol'skii and S. E. Savel'ev and Franco Nori},
journal= {arXiv preprint arXiv:0712.1407},
year = {2007}
}