Band gaps in graphene via periodic electrostatic gating

Abstract

Much attention has been focused on ways of rendering graphene semiconducting. We study periodically gated graphene in a tight-binding model and find that, contrary to predictions based on the Dirac equation, it is possible to open a band gap at the Fermi level using electrostatic gating of graphene. However, comparing to other methods of periodically modulating graphene, namely perforated graphene structures, we find that the resulting band gap is significantly smaller. We discuss the intricate dependence of the band gap on the magnitude of the gate potential as well as the exact geometry of the edge of the gate region. The role of the overlap of the eigenstates with the gate region is elucidated. Considering more realistic gate potentials, we find that introducing smoothing in the potential distribution, even over a range of little more than a single carbon atom, reduces the attainable band gap significantly.

9 pages, 9 figures

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• Electronic Properties of Disordered Graphene Antidot Lattices
• Electronic transport in disordered graphene antidot lattice devices
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• Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions
• Electronic and optical properties of graphene antidot lattices: Comparison of Dirac and tight-binding models
• Graphene on graphene antidot lattices: Electronic and transport properties
• Tunable valley Hall effect in gate-defined graphene superlattices
• Robust band gap and half-metallicity in graphene with triangular perforations
• On the zero-field orbital magnetic susceptibility of Bloch electrons in graphene-like solids: Some rigorous results
• Boron and nitrogen doping in graphene antidot lattices
• Regularity of the density of states for random Dirac operators
• Band engineering aided by topological edge state proximity effects: Inducing anti-chirality in graphene