Lithographic band structure engineering of graphene


Two-dimensional materials such as graphene allow direct access to the entirety of atoms constituting the crystal. While this makes shaping by lithography particularly attractive as a tool for band structure engineering through quantum confinement effects, edge disorder and contamination have so far limited progress towards experimental realization. Here, we define a superlattice in graphene encapsulated in hexagonal boron nitride, by etching an array of holes through the heterostructure with minimum feature sizes of 12–15 nm. We observe a magnetotransport regime that is distinctly different from the characteristic Landau fan of graphene, with a sizeable bandgap that can be tuned by a magnetic field. The measurements are accurately described by transport simulations and analytical calculations. Finally, we observe strong indications that the lithographically engineered band structure at the main Dirac point is cloned to a satellite peak that appears due to moiré interactions between the graphene and the encapsulating material.

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Fig. 1: Charge carrier mobility μ versus minimum feature size w for nanostructured graphene reported in the literature.
Fig. 2: Device architecture and transport data for pristine and nanostructured graphene.
Fig. 3: Comparison of magnetotransport in pristine and nanostructured graphene.
Fig. 4: Magnetotransport and bandgap tuning.
Fig. 5: Cloning of engineered band structure.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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The authors thank G. Calogero, J. Handberg, J. Martiny, K. Kaasbjerg and A. Gejl for discussions. The Center for Nanostructured Graphene (CNG) is sponsored by the Danish National Research Foundation, Project DNRF103. B.S.J., L.G., J.M.C. and P.B. acknowledge funding from EU H2020 ‘Graphene Flagship’, grant agreements 696656 (Core 1) and 785219 (Core 2). T.G.P. and M.R.T. also acknowledge support for the VKR Center of Excellence QUSCOPE by the Villum Foundation. D.M.A.M. acknowledges Villum Fonden project no. VKR023117 and EC Graphene FET Flagship contract no. 785219. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT (Japan), JSPS KAKENHI grants nos. JP18K19136 and CREST (JPMJCR15F3), JST.

Author information




B.S.J. and L.G. conceived of the project and performed device fabrication and transport measurements. B.S.J., L.G. and P.B. analysed the transport data. D.M.A.M performed and analysed the COMSOL simulations. J.M.C. and D.M.A.M. advised on measurements. J.D.T, E.D. and T.J.B. assisted with device fabrication. M.R.T. and T.G.P. performed simulations and developed the analytical model. K.W. and T.T. synthesized the hBN crystals. P.B. and A.-P.J advised on the project. B.S.J., L.G., A.-P.J. and P.B. wrote the manuscript in consultation with all other authors.

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Correspondence to Peter Bøggild.

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Lithographic band structure engineering of graphene

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Jessen, B.S., Gammelgaard, L., Thomsen, M.R. et al. Lithographic band structure engineering of graphene. Nat. Nanotechnol. 14, 340–346 (2019).

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