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Resonant tunnelling between the chiral Landau states of twisted graphene lattices

Abstract

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.

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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.

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Acknowledgements

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).

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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.

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Correspondence to L. Eaves.

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The authors declare no competing financial interests.

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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). https://doi.org/10.1038/nphys3507

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