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Effective Hamiltonian for electron waves in artificial graphene: A first-principles derivation

Lannebère, S. ; Silveirinha, M. G.

Physical Review B Vol. 91, Nº 045416, pp. 1 - 16, January, 2015.

ISSN (print): 1098-0121
ISSN (online): 1098-0121

Journal Impact Factor: 3,736 (in 2014)

Digital Object Identifier: 10.1103/PhysRevB.91.045416

Abstract
We propose a first-principles effective medium formalism to study the propagation of electron waves in semiconductor heterostructures with a zero band gap. Our theory confirms that near the K point the dynamics of a two-dimensional electron gas modulated by an external electrostatic potential with honeycomb symmetry
is described by the same pseudospinor formalism and Dirac massless equation as a graphene monolayer.
Furthermore, we highlight that even though other superlattices based on semiconductors with a zincblende-type structure can have a zero band-gap and a linear energy-momentum dispersion, the corresponding effective medium Hamiltonian is rather different from that of graphene, and can be based on a single-component wave function.