Lithographic band structure engineering of graphene

Abstract

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.

References

  1. 1.

    Dean, C. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).

    CAS  Article  Google Scholar 

  2. 2.

    Ponomarenko, L. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

    CAS  Article  Google Scholar 

  3. 3.

    Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

    CAS  Article  Google Scholar 

  4. 4.

    Forsythe, C. et al. Band structure engineering of 2D materials using patterned dielectric superlattices. Nat. Nanotechnol. 13, 566–571 (2018).

    CAS  Article  Google Scholar 

  5. 5.

    Caridad, J. M., Connaughton, S., Ott, C., Weber, H. B. & Krstić, V. An electrical analogy to Mie scattering. Nat. Commun. 7, 12894 (2016).

    CAS  Article  Google Scholar 

  6. 6.

    Stampfer, C. et al. Energy gaps in etched graphene nanoribbons. Phys. Rev. Lett. 102, 056403 (2009).

    CAS  Article  Google Scholar 

  7. 7.

    Banszerus, L. et al. Ballistic transport exceeding 28 μm in CVD grown graphene. Nano Lett. 16, 1387–1391 (2016).

    CAS  Article  Google Scholar 

  8. 8.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    CAS  Article  Google Scholar 

  9. 9.

    Zeng, Y. et al. High quality magnetotransport in graphene using the edge-free Corbino geometry. Preprint at https://arxiv.org/abs/1805.04904 (2018).

  10. 10.

    Polshyn, H. et al. Quantitative transport measurements of fractional quantum Hall energy gaps in edgeless graphene devices. Preprint at https://arxiv.org/abs/1805.04199 (2018).

  11. 11.

    Barone, V., Hod, O. & Scuseria, G. E. Electronic structure and stability of semiconducting graphene nanoribbons. Nano Lett. 6, 2748–2754 (2006).

    CAS  Article  Google Scholar 

  12. 12.

    Sandner, A. et al. Ballistic transport in graphene antidot lattices. Nano Lett. 15, 8402–8406 (2015).

    CAS  Article  Google Scholar 

  13. 13.

    Yagi, R. et al. Ballistic transport in graphene antidot lattices. Phys. Rev. B 92, 195406 (2015).

    Article  Google Scholar 

  14. 14.

    Han, M. Y., Brant, J. C. & Kim, P. Electron transport in disordered graphene nanoribbons. Phys. Rev. Lett. 104, 056801 (2010).

    Article  Google Scholar 

  15. 15.

    Fang, T., Konar, A., Xing, H. & Jena, D. Mobility in semiconducting graphene nanoribbons: phonon, impurity, and edge roughness scattering. Phys. Rev. B 78, 205403 (2008).

    Article  Google Scholar 

  16. 16.

    Yang, Y. & Murali, R. Impact of size effect on graphene nanoribbon transport. IEEE Electron. Dev. Lett. 31, 237–239 (2010).

    Article  Google Scholar 

  17. 17.

    Bang, K. et al. Effect of ribbon width on electrical transport properties of graphene nanoribbons. Nano Converg. 5, 7 (2018).

    Article  Google Scholar 

  18. 18.

    Kim, M., Safron, N. S., Han, E., Arnold, M. S. & Gopalan, P. Fabrication and characterization of large-area, semiconducting nanoperforated graphene materials. Nano Lett. 10, 1125–1131 (2010).

    CAS  Article  Google Scholar 

  19. 19.

    Mackenzie, D. M. A. et al. Graphene antidot lattice transport measurements. Int. J. Nanotechnol. 14, 226–234 (2017).

    CAS  Article  Google Scholar 

  20. 20.

    Mackenzie, D. M. A. et al. Batch fabrication of nanopatterned graphene devices via nanoimprint lithography. Appl. Phys. Lett. 111, 193103 (2017).

    Article  Google Scholar 

  21. 21.

    Wang, M. et al. CVD growth of large area smooth-edged graphene nanomesh by nanosphere lithography. Sci. Rep. 3, 1238 (2013).

    Article  Google Scholar 

  22. 22.

    Peters, E., Giesbers, A., Zeitler, U., Burghard, M. & Kern, K. Valley-polarized massive charge carriers in gapped graphene. Phys. Rev. B 87, 201403 (2013).

    Article  Google Scholar 

  23. 23.

    Pan, J. et al. Berry curvature and nonlocal transport characteristics of antidot graphene. Phys. Rev. X 7, 031043 (2017).

    Google Scholar 

  24. 24.

    Pizzocchero, F. et al. The hot pick-up technique for batch assembly of van der Waals heterostructures. Nat. Commun. 7, 11894 (2016).

    CAS  Article  Google Scholar 

  25. 25.

    Terrés, B. et al. Size quantization of Dirac fermions in graphene constrictions. Nat. Commun. 7, 11528 (2016).

    Article  Google Scholar 

  26. 26.

    Power, S. R., Thomsen, M. R., Jauho, A.-P. & Pedersen, T. G. Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions. Phys. Rev. B 96, 075425 (2017).

    Article  Google Scholar 

  27. 27.

    Drienovsky, M. et al. Commensurability oscillations in one-dimensional graphene superlattices. Phys. Rev. Lett. 121, 026806 (2018).

    CAS  Article  Google Scholar 

  28. 28.

    Thomsen, M. R. & Pedersen, T. G. Analytical Dirac model of graphene rings, dots, and antidots in magnetic fields. Phys. Rev. B 95, 235427 (2017).

    Article  Google Scholar 

  29. 29.

    Pedersen, T. G. et al. Graphene antidot lattices: designed defects and spin qubits. Phys. Rev. Lett. 100, 136804 (2008).

    Article  Google Scholar 

  30. 30.

    Pedersen, J. G. & Pedersen, T. G. Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices. Phys. Rev. B 87, 235404 (2013).

    Article  Google Scholar 

  31. 31.

    Thomsen, M. R., Power, S. R., Jauho, A.-P. & Pedersen, T. G. Magnetic edge states and magnetotransport in graphene antidot barriers. Phys. Rev. B 94, 045438 (2016).

    Article  Google Scholar 

  32. 32.

    Heydrich, S. et al. Scanning Raman spectroscopy of graphene antidot lattices: evidence for systematic p-type doping. Appl. Phys. Lett. 97, 043113 (2010).

    Article  Google Scholar 

  33. 33.

    Sarma, S. D. & Hwang, E. Two-dimensional metal–insulator transition as a strong localization induced crossover phenomenon. Phys. Rev. B 89, 235423 (2014).

    Article  Google Scholar 

  34. 34.

    Radisavljevic, B. & Kis, A. Mobility engineering and a metal–insulator transition in monolayer MoS2. Nat. Mater. 12, 815–820 (2013).

    CAS  Article  Google Scholar 

  35. 35.

    Shimizu, T. et al. Large intrinsic energy bandgaps in annealed nanotube-derived graphene nanoribbons. Nat. Nanotechnol. 6, 45–50 (2011).

    CAS  Article  Google Scholar 

  36. 36.

    Gorbachev, R. et al. Detecting topological currents in graphene superlattices. Science 346, 448–451 (2014).

    CAS  Article  Google Scholar 

  37. 37.

    Eroms, J. & Weiss, D. Weak localization and transport gap in graphene antidot lattices. New J. Phys. 11, 095021 (2009).

    Article  Google Scholar 

  38. 38.

    Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).

    CAS  Article  Google Scholar 

  39. 39.

    Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    CAS  Article  Google Scholar 

  40. 40.

    Novoselov, K. S. et al. Room-temperature quantum Hall effect in graphene. Science 315, 1379–1379 (2007).

    CAS  Article  Google Scholar 

  41. 41.

    Svizhenko, A., Anantram, M., Govindan, T., Biegel, B. & Venugopal, R. Two-dimensional quantum mechanical modeling of nanotransistors. J. Appl. Phys. 91, 2343–2354 (2002).

    CAS  Article  Google Scholar 

  42. 42.

    Lewenkopf, C. H. & Mucciolo, E. R. The recursive Green’s function method for graphene. J. Comput. Electron. 12, 203–231 (2013).

    CAS  Article  Google Scholar 

  43. 43.

    Weiss, D., Klitzing, K. V., Ploog, K. & Weimann, G. Magnetoresistance oscillations in a two-dimensional electron gas induced by a submicrometer periodic potential. Europhys. Lett. 8, 179–184 (1989).

    CAS  Article  Google Scholar 

  44. 44.

    Park, C.-H., Yang, L., Son, Y.-W., Cohen, M. L. & Louie, S. G. New generation of massless Dirac fermions in graphene under external periodic potentials. Phys. Rev. Lett. 101, 126804 (2008).

    Article  Google Scholar 

  45. 45.

    Kindermann, M., Uchoa, B. & Miller, D. L. Zero-energy modes and gate-tunable gap in graphene on hexagonal boron nitride. Phys. Rev. B 86, 115415 (2012).

    Article  Google Scholar 

  46. 46.

    Wallbank, J., Patel, A., Mucha-Kruczyński, M., Geim, A. & Fal’ko, V. Generic miniband structure of graphene on a hexagonal substrate. Phys. Rev. B 87, 245408 (2013).

    Article  Google Scholar 

  47. 47.

    Lee, M. et al. Ballistic miniband conduction in a graphene superlattice. Science 353, 1526–1529 (2016).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

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.

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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). https://doi.org/10.1038/s41565-019-0376-3

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