Dirac spectrum in piecewise constant one-dimensional (1D) potentials

D. P. Arovas, L. Brey, H. A. Fertig, Eun Ah Kim, K. Ziegler

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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 that 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.

Original languageEnglish
Article number123020
JournalNew Journal of Physics
StatePublished - Dec 2010


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