Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

Abstract

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.

10 pages, 12 figures, additional references added

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• Moire superlattice effects in graphene/boron-nitride van der Waals heterostructures
• Transport in superlattices on single layer graphene
• Controlling the energy gap of graphene by Fermi velocity engineering
• Band structure and gaps of triangular graphene superlattices
• Graphene superlattice with periodically modulated Dirac gap
• Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes
• Electronic structure of a graphene superlattice with massive Dirac fermions
• Graphene: Kinks, Superlattices, Landau levels, and Magnetotransport
• Topological effects and particle-physics analogies beyond the massless Dirac-Weyl fermion in graphene nanorings
• Non-local quantum effects in plasmons of graphene superlattices
• Dirac point formation revealed by Andreev tunneling in superlattice-graphene/superconductor junctions
• Tunneling states in graphene heterostructures consisting of two different graphene superlattices
• Signatures of evanescent mode transport in graphene
• Transport in Graphene superimposed by a moving Electrical Superlattice Potential
• Semiclassical Approach to the Physics of Smooth Superlattice Potentials in Graphene
• Effect of weak disorder on delocalization properties of gapped graphene superlattices
• Zener tunneling isospin Hall effect in HgTe quantum wells and graphene multilayers
• Strong Enhancement of High Voltage Electronic Transport in Chiral Electrical Nanotube Superlattices
• Electron Transmission Across Normal Metal-Strained Graphene-Normal Metal Junctions
• A Green's function approach to transmission of massless Dirac fermions in graphene through an array of random scatterers
• The selection rule of graphene in a composite magnetic field
• Scaling behavior of disordered lattice fermions in two dimensions
• Band Structure and Topological Properties of Graphene in a Superlattice Spin Exchange Field