Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

Details Dirac Spectrum in Piecewise Constant One-Dimensional Potentials Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

2010-02-19

arxiv.org/abs/1002.3655v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 12 figures, additional references added

Scientific paper

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.

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