Time Evolution of Electron Waves in Graphene Superlattices

TL;DR

This paper investigates how electron waves evolve over time in graphene superlattices, demonstrating that a simplified effective medium approach accurately describes transport in many scenarios, even with complex potentials or interfaces.

Contribution

It shows that the continuum approximation is valid for electron transport in graphene superlattices under various conditions, simplifying analysis and modeling.

Findings

Effective Hamiltonian accurately describes electron transport.

Continuum approximation holds for less localized initial states.

Electrons in anisotropic superlattices experience minimal diffraction.

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.