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See supplementary material at http://dx.doi.org/10.1063/1.4959190 for (i) validation of the FDTD algorithm in simple graphene heterostructures, (ii) the time animations of the electronic states propagating in the graphene superlattices for the examples of Figs. 8(b), 8(c) and 8(d).[Supplementary Material]
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/content/aip/journal/adva/6/7/10.1063/1.4959190
2016-07-15
2016-12-08

Abstract

The time evolution of electron waves in graphene superlattices is studied using both microscopic and “effective medium” formalisms. The numerical simulations reveal that in a wide range of physical scenarios it is possible to neglect the granularity of the superlattice and characterize the electron transport using a simple effective Hamiltonian. It is verified that as general rule the continuum approximation is rather accurate when the initial state is less localized than the characteristic spatial period of the superlattice. This property holds even when the microsocopic electric potential has a strong spatial modulation or in presence of interfaces between different superlattices. Detailed examples are given both of the time evolution of initial electronic states and of the propagation of stationary states in the context of wave scattering. The theory also confirms that electrons propagating in tailored graphene superlattices with extreme anisotropy experience virtually no diffraction.

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