{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:07:19Z","timestamp":1753873639139,"version":"3.41.2"},"reference-count":52,"publisher":"AIP Publishing","issue":"7","license":[{"start":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T00:00:00Z","timestamp":1468540800000},"content-version":"vor","delay-in-days":14,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T00:00:00Z","timestamp":1468540800000},"content-version":"tdm","delay-in-days":14,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2016,7,1]]},"abstract":"<jats:p>The time evolution of electron waves in graphene superlattices is studied using both microscopic and \u201ceffective medium\u201d 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.<\/jats:p>","DOI":"10.1063\/1.4959190","type":"journal-article","created":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T17:09:36Z","timestamp":1468602576000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Time evolution of electron waves in graphene superlattices"],"prefix":"10.1063","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7171-1879","authenticated-orcid":false,"given":"David E.","family":"Fernandes","sequence":"first","affiliation":[{"name":"University of Coimbra 1 Instituto de Telecomunica\u00e7\u00f5es and Department of Electrical Engineering, , 3030-290, Coimbra, Portugal"}]},{"given":"Manuel","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"University of Coimbra 1 Instituto de Telecomunica\u00e7\u00f5es and Department of Electrical Engineering, , 3030-290, Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9805-6747","authenticated-orcid":false,"given":"Gabriel","family":"Falc\u00e3o","sequence":"additional","affiliation":[{"name":"University of Coimbra 1 Instituto de Telecomunica\u00e7\u00f5es and Department of Electrical Engineering, , 3030-290, Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3730-1689","authenticated-orcid":false,"given":"M\u00e1rio G.","family":"Silveirinha","sequence":"additional","affiliation":[{"name":"University of Coimbra 1 Instituto de Telecomunica\u00e7\u00f5es and Department of Electrical Engineering, , 3030-290, Coimbra, Portugal"},{"name":"Instituto Superior T\u00e9cnico-University of Lisbon 2 , Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2016,7,15]]},"reference":[{"key":"2023071501240360600_c1","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1038\/nature04233","article-title":"Two-dimensional gas of massless Dirac fermions in graphene","volume":"438","year":"2005","journal-title":"Nature"},{"key":"2023071501240360600_c2","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1038\/nmat1849","article-title":"The rise of graphene","volume":"6","year":"2007","journal-title":"Nature Mater."},{"key":"2023071501240360600_c3","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1103\/RevModPhys.81.109","article-title":"The electronic properties of graphene","volume":"81","year":"2009","journal-title":"Rev. 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