Linear magnetoresistance in mosaic-like bilayer graphene

Journal name:
Nature Physics
Year published:
Published online

The magnetoresistance of conductors usually has a quadratic dependence on magnetic field1, however, examples exist of non-saturating linear behaviour in diverse materials2, 3, 4, 5, 6. Assigning a specific microscopic mechanism to this unusual phenomenon is obscured by the co-occurrence and interplay of doping, mobility fluctuations and a polycrystalline structure7, 8. Bilayer graphene has virtually no doping fluctuations, yet provides a built-in mosaic tiling due to the dense network of partial dislocations9, 10. We present magnetotransport measurements of epitaxial bilayer graphene that exhibits a strong and reproducible linear magnetoresistance that persists to B = 62 T at and above room temperature, decorated by quantum interference effects at low temperatures. Partial dislocations thus have a profound impact on the transport properties in bilayer graphene, a system that is frequently assumed to be dislocation-free. It further provides a clear and tractable model system for studying the unusual properties of mosaic conductors.

At a glance


  1. Experimental data of linear MR.
    Figure 1: Experimental data of linear MR.

    a, In large-area bilayer graphene (the scanning electron micrograph (SEM) of a Hall bar is shown in the inset, together with a close-up that shows mainly bilayer, but also trilayer strips as darker shaded areas), a strong linear MR contribution appears in addition to the temperature-dependent WL and EEI corrections similarly observed in monolayer graphene. b, MR measured in pulsed magnetic fields, showing non-saturating linear behaviour up to 62 T at room temperature, with quantum deviations at lower temperatures (data have been vertically shifted by 20 for better visibility). c,d, A smaller, pure bilayer sample exhibits linear MR and further periodic quantum interference fluctuations at low temperatures (c), the Fourier spectrum of which shows a correlation field of Bc = 0.55 T, indicated by the arrow (d). Inset in d is a SEM image of the sample showing the absence of trilayer areas.

  2. From network structure to linear MR.
    Figure 2: From network structure to linear MR.

    a, Partial dislocation network in a bilayer membrane originating from epitaxial graphene on SiC(0001). The image shows a composite (or superposition) of three dark-field TEM images, taken with the three reflections, such that the full network of partial dislocations is revealed, providing the mosaic tiling of bilayer graphene. b, Partial dislocation network in which the colour encodes the crystallographic Burgers vector associated with the partial dislocations as extracted from the individual dark-field TEM data (red square in a)10. c, Probability | Ψ |2 of a network eigenstate, which for clarity we select close to the Dirac point (the energy of the eigenstate is indicated by the dashed vertical line in d); segmentation of the network state on the AB/AC tiles is evident. d, Spectral weight of the monolayer graphene states present in the network state; for a perfect AB bilayer only two such states would be present. e, This motivates the classical model of a network of three-terminal interconnected conductive discs, for which at finite magnetic field the resulting potential landscape (colour map) and non-trivial current distribution (green arrows) resembles that found for the four-terminal case7. f, Comparison of MR for a (4 × 3) network (see e) with a similar but larger (32 × 24) network, for which we assumed a charge carrier density of 6 × 1012 cm−2 and a mobility of 10,000 cm2 V −1 s−1. The first value is measured, whereas the second is a reasonable assumption that gives a crossover field to linear MR similar to experiments.


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  1. Lehrstuhl für Angewandte Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7 91058 Erlangen, Germany

    • Ferdinand Kisslinger,
    • Christian Ott,
    • Christian Heide &
    • Heiko B. Weber
  2. Dresden High Magnetic Field Laboratory, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400 01328 Dresden, Germany

    • Erik Kampert
  3. Lehrstuhl für Mikro- und Nanostrukturforschung & Center for Nanoanalysis and Electron Microscopy (CENEM), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstraße 6 91058 Erlangen, Germany

    • Benjamin Butz &
    • Erdmann Spiecker
  4. Lehrstuhl für Theoretische Festkörperphysik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7 91058 Erlangen, Germany

    • Sam Shallcross


F.K. and H.B.W. conceived the experiment. F.K. and C.O. carried out sample preparation, electrical measurement and data analysis, supported by C.H. in an early stage. F.K. and E.K. carried out high magnetic field measurements. B.B. and E.S. contributed structural information on dislocation networks by TEM. The quantum mechanical calculations were developed and performed by S.S. Network simulation was performed by F.K. and C.O. The manuscript was written by F.K., C.O., S.S. and H.B.W. All authors discussed the results and implications and commented on the manuscript at all stages.

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