Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Resonant tunnelling between the chiral Landau states of twisted graphene lattices


A class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An exemplar of such a structure is a transistor device in which relativistic Dirac fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantizes graphene’s gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau-level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following an inter-layer tunnelling event, is analogous to the case of intra-layer Klein tunnelling.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Figure 1: Device structure and misaligned Brillouin zones.
Figure 2: Magnetic field-induced resonances in the conductance.
Figure 3: Differential magnetoconductance maps: experiment and theory.
Figure 4: Energy alignment and tunnelling rates between the Landau levels of the two graphene electrodes.
Figure 5: Effect of chirality on the differential magnetoconductance: experiment and theory.
Figure 6: Electron wavefunctions and semiclassical cyclotron orbits in the two graphene layers for figure-of-8 and nested tunnelling transitions.


  1. Liu, Y., Bian, G., Miller, T. & Chiang, T.-C. Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light. Phys. Rev. Lett. 107, 166803 (2011).

    Article  ADS  Google Scholar 

  2. Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620–625 (2006).

    Article  ADS  Google Scholar 

  3. Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Phys. 5, 222–226 (2009).

    Article  ADS  Google Scholar 

  4. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  Google Scholar 

  5. Britnell, L. et al. Field-effect tunneling transistor based on vertical graphene heterostructures. Science 335, 947–950 (2012).

    Article  ADS  Google Scholar 

  6. Mishchenko, A. et al. Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures. Nature Nanotech. 9, 808–813 (2014).

    Article  ADS  Google Scholar 

  7. Fallahazad, B. et al. Gate-tunable resonant tunneling in double bilayer graphene heterostructures. Nano Lett. 15, 428–433 (2015).

    Article  ADS  Google Scholar 

  8. Britnell, L. et al. Resonant tunnelling and negative differential conductance in graphene transistors. Nature Commun. 4, 1794 (2013).

    Article  ADS  Google Scholar 

  9. Feenstra, R. M., Jena, D. & Gu, G. Single-particle tunneling in doped graphene–insulator–graphene junctions. J. Appl. Phys. 111, 043711 (2012).

    Article  ADS  Google Scholar 

  10. Zhao, P., Feenstra, R. M., Gu, G. & Jena, D. SymFET: A proposed symmetric graphene tunneling field-effect transistor. IEEE Trans. Electron Devices 60, 951–957 (2013).

    Article  ADS  Google Scholar 

  11. Brey, L. Coherent tunneling and negative differential conductivity in a graphene/h-BN/graphene heterostructure. Phys. Rev. Appl. 2, 014003 (2014).

    Article  ADS  Google Scholar 

  12. Vasko, F. T. Resonant and nondissipative tunneling in independently contacted graphene structures. Phys. Rev. B 87, 075424 (2013).

    Article  ADS  Google Scholar 

  13. Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Coulomb barrier to tunneling between parallel two-dimensional electron systems. Phys. Rev. Lett. 69, 3804 (1992).

    Article  ADS  Google Scholar 

  14. Leadbeater, M. L., Sheard, F. W. & Eaves, L. Inter-Landau-level transitions of resonantly tunnelling electrons in tilted magnetic fields. Semicond. Sci. Technol. 6, 1021–1024 (1991).

    Article  ADS  Google Scholar 

  15. Lee, G. H. et al. Electron tunneling through atomically flat and ultrathin hexagonal boron nitride. Appl. Phys. Lett. 99, 243114 (2011).

    Article  ADS  Google Scholar 

  16. Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: Electronic structure. Phys. Rev. Lett. 99, 256802 (2007).

    Article  ADS  Google Scholar 

  17. Mele, E. J. Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405 (2010).

    Article  ADS  Google Scholar 

  18. Bistritzer, R. & MacDonald, A. H. Transport between twisted graphene layers. Phys. Rev. B 81, 245412 (2010).

    Article  ADS  Google Scholar 

  19. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 122337 (2011).

    Article  Google Scholar 

  20. Shon, N. & Ando, T. Quantum transport in two-dimensional graphite system. J. Phys. Soc. Jpn 67, 2421–2429 (1998).

    Article  ADS  Google Scholar 

  21. Zheng, Y. & Ando, T. Hall conductivity of a two-dimensional graphite system. Phys. Rev. B 65, 245420 (2002).

    Article  ADS  Google Scholar 

  22. 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).

    Article  ADS  Google Scholar 

  23. Li, G., Luican, A. & Andrei, E. Y. Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009).

    Article  ADS  Google Scholar 

  24. Fu, Y.-S. et al. Imaging the two-component nature of Dirac–Landau levels in the topological surface state of Bi2Se3 . Nature Phys. 10, 815–819 (2014).

    Article  ADS  Google Scholar 

  25. Miller, D. L. et al. Real-space mapping of magnetically quantized graphene states. Nature Phys. 6, 811–817 (2010).

    Article  ADS  Google Scholar 

  26. Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 136806 (2006).

    Article  ADS  Google Scholar 

  27. Li, G., Luican-Mayer, A., Abanin, D., Levitov, L. & Andrei, E. Y. Evolution of Landau levels into edge states in graphene. Nature Commun. 4, 1744 (2013).

    Article  ADS  Google Scholar 

  28. Luican-Mayer, A. et al. Screening charged impurities and lifting the orbital degeneracy in graphene by populating Landau levels. Phys. Rev. Lett. 112, 036804 (2013).

    Article  ADS  Google Scholar 

  29. Ponomarenko, L. A. et al. Density of states and zero Landau level probed through capacitance of graphene. Phys. Rev. Lett. 105, 136801 (2010).

    Article  ADS  Google Scholar 

  30. Pratley, L. & Zülicke, U. Magnetotunneling spectroscopy of chiral two-dimensional electron systems. Phys. Rev. B 88, 245412 (2013).

    Article  ADS  Google Scholar 

  31. Pratley, L. & Zülicke, U. Valley filter from magneto-tunneling between single and bi-layer graphene. Appl. Phys. Lett. 104, 082401 (2014).

    Article  ADS  Google Scholar 

  32. Pershoguba, S. S., Abergel, D. S. L., Yakovenko, V. M. & Balatsky, A. V. Effects of a tilted magnetic field in a Dirac double layer. Phys. Rev. B 91, 085418 (2015).

    Article  ADS  Google Scholar 

Download references


This work was supported by the EU Graphene Flagship Programme and ERC Synergy Grant, Hetero2D. M.T.G. acknowledges The Leverhulme Trust for support of an Early Career Fellowship. V.I.F. acknowledges support of a Royal Society Wolfson Research Merit Award. E.E.V. and S.V.M. were supported by NUST ”MISiS” (grant K1-2015-046) and RFBR (15-02-01221 and 14-02-00792).

Author information

Authors and Affiliations



Y.C. and A.V.K., fabricated the devices. E.E.V., A.M., O.M., A.P., K.S.N., A.V.K., M.J.Z. and L.E., designed and/or carried out the experiments. M.T.G., T.M.F., L.E., E.E.V., A.M., S.V.M., J.R.W., V.I.F., K.S.N. and A.K.G., undertook the interpretation of the data. M.T.G. performed the calculations. M.T.G., T.M.F. and L.E. wrote the manuscript with contributions from the other authors.

Corresponding author

Correspondence to L. Eaves.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2438 kb)

Supplementary Movie

Supplementary Movie 1 (AVI 4890 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Greenaway, M., Vdovin, E., Mishchenko, A. et al. Resonant tunnelling between the chiral Landau states of twisted graphene lattices. Nature Phys 11, 1057–1062 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing