Limitations of effective medium theory in multilayer graphite/hBN heterostructures

René Petersen, Thomas Garm Pedersen, Morten Niklas Gjerding, Kristian Sommer Thygesen

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We apply effective medium theory (EMT) to metamaterials consisting of a varying number of consecutive sheets of graphene and hexagonal boron nitride, and compare this with a full calculation of the permittivity and the reflection based on the tight binding method and the transfer matrix method in order to study the convergence to EMT.We find that convergence is reached for both in-plane and out-of-plane directions already for five sheets but that for≈30 sheets multiple reflection effects causes the reflection spectrum to differ from EMT.We show that
modes that are evanescent in air are extremely sensitive to the electronic details of the sheets near the structure boundary and that EMT estimates poorly the reflection of these modes, causing an overestimation of the Purcell factor. Finally, we offer an improved EMT, which gives far better convergence in the low-energy regime.
Original languageEnglish
Article number035128
JournalPhysical Review B
Issue number3
Number of pages10
Publication statusPublished - 2016


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