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Coherent commensurate electronic states at the interface between misoriented graphene layers


Graphene and layered materials in general exhibit rich physics and application potential owing to their exceptional electronic properties, which arise from the intricate π-orbital coupling and the symmetry breaking in twisted bilayer systems1,2,3,4,5,6,7,8,9,10,11,12,13,14. Here, we report room-temperature experiments to study electrical transport across a bilayer graphene interface with a well-defined rotation angle between the layers that is controllable in situ. This twisted interface is artificially created in mesoscopic pillars made of highly oriented pyrolytic graphite by mechanical actuation. The overall measured angular dependence of the conductivity is consistent with a phonon-assisted transport mechanism that preserves the electron momentum of conduction electrons passing the interface15. The most intriguing observations are sharp conductivity peaks at interlayer rotation angles of 21.8° and 38.2°. These angles correspond to a commensurate crystalline superstructure leading to a coherent two-dimensional (2D) electronic interface state. Such states, predicted by theory16,17, form the basis for a new class of 2D weakly coupled bilayer systems with hitherto unexplored properties and applications.

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Figure 1: Experimental procedure.
Figure 2: Interlayer conductivity.
Figure 3: Commensurate twisted configurations.
Figure 4: Momentum-space representation of bilayer graphene coupling at commensurate twist angles θ = 21.8° and 38.2°.


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We thank U. Drechsler and M. Tschudy for invaluable technical support and J. Tersoff, V. Perebeinos, N. Moll and R. Allenspach for stimulating discussions. The work was supported by the FP7 Marie Curie Actions of the European Commission, ITN fellowship cQOM (Project ID 290161) and by the Swiss National Science Foundation, Ambizione Grant No. PZ00P2 161388 (E.K.). Work at TAU was supported by the Israel Science Foundation under grant No. 1740/13, the Lise-Meitner Minerva Center for Computational Quantum Chemistry, and the Center for Nanoscience and Nanotechnology at Tel-Aviv University.

Author information




E.K., A.K. and U.D. jointly conceived the experimental concept. E.K. performed the experimental work including reactive ion etching, AFM characterization, electrical transport measurements and data analysis. E.K. also participated in the writing of the manuscript. A.K. provided operational guidance for the AFM. E.L. was responsible for the electron beam lithography and metal lift-off process for the fabrication of the metal masks. U.D. was responsible for the writing of the manuscript. I.L. participated in the development of the global (GRI) and local (LRI) registry index concept and implemented them within a computational code. I.L. also performed the numerical calculations of the GRI, LRI and interlayer transport and participated in the writing of the manuscript. O.H. conceived the concept of the GRI and LRI, developed and implemented the interlayer transport code and participated in the writing of the manuscript.

Corresponding authors

Correspondence to Elad Koren or Urs Duerig.

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The authors declare no competing financial interests.

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Koren, E., Leven, I., Lörtscher, E. et al. Coherent commensurate electronic states at the interface between misoriented graphene layers. Nature Nanotech 11, 752–757 (2016).

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