An Effective Medium Approach to Electron Waves: Graphene Superlattices

Abstract

We develop an effective medium approach to characterize the propagation of matter waves in periodic structures, such as graphene or semiconductor superlattices. It is proven that the time evolution of the states that are not more localized in space than the characteristic period of the structure can be described exactly through an effective Hamiltonian, and that the electronic band structure of the system can be exactly determined from the effective Hamiltonian. As an illustration of the application of the method, we characterize the mesoscopic response of graphene superlattices. It is shown that these structures may be described using simply two effective parameters: a dispersive potential, and an anisotropy tensor that characterizes the pseudospin. Our model predicts that a graphene superlattice characterized by an indefinite anisotropy tensor - such that the eigenvalues of the tensor have opposite signs - may permit the perfect tunneling of all the stationary states with a specific value of the energy when it is paired with a dual graphene superlattice with positive definite anisotropy tensor.

36 pages

References in corpus (7)

• The electronic properties of graphene
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• First-Principle Homogenization Theory for Periodic Metamaterials
• Electronic properties of mesoscopic graphene structures: charge confinement and control of spin and charge transport
• Electron Beam Supercollimation in Graphene Superlattices
• Transformation Electronics: Tailoring Electron's Effective Mass

Cited by in corpus (11)

• Electronic beam shifts in monolayer graphene superlattice
• Link between the photonic and electronic topological phases in artificial graphene
• Homogenization of Dispersive Spacetime Crystals: Anomalous Dispersion and Negative Stored Energy
• Effective Hamiltonian for electron waves in artificial graphene: A first principles derivation
• A Metamaterial-Inspired Model for Electron Waves in Bulk Semiconductors
• Embedded Energy State in an Open Semiconductor Heterostructure
• Giant nonlinearity in Zero-Gap Semiconductor Superlattices
• A Perfect Lens for Ballistic Electrons: A Kane's Model
• Time Evolution of Electron Waves in Graphene Superlattices
• Effective Medium Model for Graphene Superlattices with Electrostatic and Magnetic Vector Potentials
• A graphene inspired electromagnetic superlens