Dirac-Schrodinger transformations in contacted graphene structures

Abstract

At an interface between contacts and graphene, the mathematical equation that governs the propagation of electrons transforms from the Schrodinger to the Dirac equation. The condition of current probability conservation at such an interface does not determine uniquely the boundary conditions for the quantum wavefunction. We discuss the possible form of boundary conditions, determine its influence on the transmission coefficient of a contacted graphene structure and suggest that optical experiments on photonic crystals with Dirac points can help identifying, under certain circumstances, the proper boundary condition at graphene- electrode interfaces.

References in corpus (5)

• The electronic properties of graphene
• Analogs of quantum Hall effect edge states in photonic crystals
• Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal
• Extremal transmission at the Dirac point of a photonic band structure
• Transmission through a boundary between monolayer and bilayer graphene

Cited by in corpus (5)

• Quantum transport across van der Waals domain walls in bilayer graphene
• A new coupling mechanism between two graphene electron waveguides for ultrafast switching
• Supercurrent reversal in Josephson junctions based on bilayer graphene flakes
• Electron Transmission Across Normal Metal-Strained Graphene-Normal Metal Junctions
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch