Electronic transport in polycrystalline graphene

Journal name:
Nature Materials
Year published:
Published online

Most materials in available macroscopic quantities are polycrystalline. Graphene, a recently discovered two-dimensional form of carbon with strong potential for replacing silicon in future electronics1, 2, 3, is no exception. There is growing evidence of the polycrystalline nature of graphene samples obtained using various techniques4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Grain boundaries, intrinsic topological defects of polycrystalline materials14, are expected to markedly alter the electronic transport in graphene. Here, we develop a theory of charge carrier transmission through grain boundaries composed of a periodic array of dislocations in graphene based on the momentum conservation principle. Depending on the grain-boundary structure we find two distinct transport behaviours—either high transparency, or perfect reflection of charge carriers over remarkably large energy ranges. First-principles quantum transport calculations are used to verify and further investigate this striking behaviour. Our study sheds light on the transport properties of large-area graphene samples. Furthermore, purposeful engineering of periodic grain boundaries with tunable transport gaps would allow for controlling charge currents without the need to introduce bulk bandgaps in otherwise semimetallic graphene. The proposed approach can be regarded as a means towards building practical graphene electronics.

At a glance


  1. Structure of grain boundaries in graphene.
    Figure 1: Structure of grain boundaries in graphene.

    a, An example of a tilt grain boundary in graphene separating two crystalline domains rotated by θ=θL+θR=8.2°+30.0°=38.2° with respect to each other. We use the convention for misorientation angles introduced in ref. 16. The repeat vector d of the grain-boundary structure is defined by the matching vectors (5, 3) and (7, 0) in the left and right domains, respectively. A possible atomic structure of the interface region involves three elementary dislocation dipoles (pentagon–heptagon pairs) per repeat cell. b, Effective rotation of the hexagonal Brillouin zone of graphene experienced by charge carriers crossing the (5,3)|(7,0) grain boundary.

  2. Grain boundaries in graphene—two distinct transport behaviours.
    Figure 2: Grain boundaries in graphene—two distinct transport behaviours.

    a, Scheme illustrating the mapping of the band structures of the two crystalline domains of graphene onto the 1D mini-Brillouin zone of the periodic grain-boundary structure. The Brillouin zones of the two graphene domains (blue and red hexagons) rotated by angles θL and θR respectively, are folded along the dotted lines , and projected onto the 1D mini-Brillouin zone of the periodic grain boundary (thick line). The actual construction corresponds to the (5,3)|(7,0) grain boundary shown in Fig. 1a. b, Position of the 2D Brillouin-zone corners K and K′ with respect to the solid lines k=2nπ/d for nm=3q and nm≠3q ( ). c, The shaded areas correspond to momentum–energy pairs for which conductance channels exist in the two crystalline domains. In the case of class Ia or class Ib grain boundaries, two and one conductance channels, respectively, are available for allowed values of k at low energies. Denser shading in the case of class Ib grain boundaries at higher energies corresponds to two conductance channels. No selection by momentum (that is, mismatch of k for states at a given energy) takes place for these two classes because identical areas of available conductance channels are superimposed. Transmission through class II grain boundaries is possible only in regions where the two colours overlap (shown in magenta), opening a transport gap Eg.

  3. Electronic transport through grain boundaries in graphene from first principles.
    Figure 3: Electronic transport through grain boundaries in graphene from first principles.

    a, Atomic structure of the (2,1)|(2,1) (θ=21.8°) class Ib grain boundary. b, Transmission probability through the (2,1)|(2,1) grain boundary as a function of transverse momentum k and energy E. c, Zero-bias total transmission per unit length through the (2,1)|(2,1) grain boundary as a function of energy (solid line) compared to the one of ideal graphene (dashed line). d, Atomic structure of the (5,0)|(3,3) (θ=30.0°) class II grain boundary. e,f, Corresponding k-resolved and total charge carrier transmissions through the (5,0)|(3,3) class II grain boundary.


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  1. Department of Physics, University of California, Berkeley, California 94720, USA

    • Oleg V. Yazyev &
    • Steven G. Louie
  2. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Oleg V. Yazyev &
    • Steven G. Louie


O.V.Y. proposed the project, carried out derivation, computations and analyses and wrote the manuscript. S.G.L. directed the research, proposed analyses, interpreted results and edited the manuscript.

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