Letter | Published:

Designer Dirac fermions and topological phases in molecular graphene

Nature volume 483, pages 306310 (15 March 2012) | Download Citation

Abstract

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials1. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms2,3,4. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system—molecular graphene—assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface5. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p–n and p–n–p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass6,7,8. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields9,10,11,12, wherein Dirac electrons react to ‘pseudo’ electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.

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References

  1. 1.

    , , , & The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)

  2. 2.

    Ultracold quantum gases in optical lattices. Nature Phys. 1, 23–30 (2005)

  3. 3.

    , & Simulation and detection of Dirac fermions with cold atoms in an optical lattice. Phys. Rev. Lett. 98, 260402 (2007)

  4. 4.

    , & Dirac-point engineering and topological phase transitions in honeycomb optical lattices. N. J. Phys. 10, 103027 (2008)

  5. 5.

    , , , & Quantum holographic encoding in a two-dimensional electron gas. Nature Nanotechnol. 4, 167–172 (2009)

  6. 6.

    et al. Irrational versus rational charge and statistics in two-dimensional quantum systems. Phys. Rev. Lett. 100, 110405 (2008)

  7. 7.

    , & Fractionalization in a square-lattice model with time-reversal symmetry. Phys. Rev. B 77, 033104 (2008)

  8. 8.

    , , & Masses in graphenelike two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics. Phys. Rev. B 80, 205319 (2009)

  9. 9.

    , & Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nature Phys. 6, 30–33 (2010)

  10. 10.

    Fractional charge from topology in polyacetylene and graphene. AIP Conf. Proc. 939, 341–350 (2007)

  11. 11.

    , & Electron fractionalization in two-dimensional graphenelike structures. Phys. Rev. Lett. 98, 186809 (2007)

  12. 12.

    & Fractional statistics of topological defects in graphene and related structures. Phys. Rev. Lett. 101, 146401 (2008)

  13. 13.

    , , , & Two- and one-dimensional honeycomb structures of silicon and germanium. Phys. Rev. Lett. 102, 236804 (2009)

  14. 14.

    et al. Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice. Science 332, 1176–1179 (2011)

  15. 15.

    , & Single-atom gating of quantum-state superpositions. Nature Phys. 4, 454–458 (2008)

  16. 16.

    et al. Quantum phase extraction in isospectral electronic nanostructures. Science 319, 782–787 (2008)

  17. 17.

    & Making massless Dirac fermions from a patterned two-dimensional electron gas. Nano Lett. 9, 1793–1797 (2009)

  18. 18.

    , & Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620–625 (2006)

  19. 19.

    , & The focusing of electron flow and a Veselago lens in graphene p-n junctions. Science 315, 1252–1255 (2007)

  20. 20.

    et al. Theory of Fano resonances in graphene: the influence of orbital and structural symmetries on STM spectra. Phys. Rev. B 81, 085413 (2010)

  21. 21.

    et al. Local electronic signatures of impurity states in graphene. Phys. Rev. B 75, 125425 (2007)

  22. 22.

    , & Midgap states and charge inhomogeneities in corrugated graphene. Phys. Rev. B 77, 075422 (2008)

  23. 23.

    & Quasiparticle scattering and local density of states in graphite. Phys. Rev. B 72, 125432 (2005)

  24. 24.

    , & Topological confinement in bilayer graphene. Phys. Rev. Lett. 100, 036804 (2008)

  25. 25.

    , & Topological delocalization of two-dimensional massless Dirac fermions. Phys. Rev. Lett. 99, 146806 (2007)

  26. 26.

    & Unconventional superconductivity on honeycomb lattice: theory of Kekule order parameter. Phys. Rev. B 82, 035429 (2010)

  27. 27.

    et al. Strain-induced pseudo-magnetic fields greater than 300 Tesla in graphene nanobubbles. Science 329, 544–547 (2010)

  28. 28.

    Pedestrian index theorem à la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene. Europhys. Lett. 87, 47008 (2009)

  29. 29.

    Pseudomagnetic catalysis of the time-reversal symmetry breaking in graphene. Phys. Rev. B 78, 205433 (2008)

  30. 30.

    et al. Band formation from coupled quantum dots formed by a nanoporous network on a copper surface. Science 325, 300–303 (2009)

Download references

Acknowledgements

This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515. F.G. acknowledges financial support from MICINN (Spain) through grants FIS2008-00124 and CONSOLIDER CSD2007-00010, and calculations supported by the US National Science Foundation. We thank C.-H. Park, I. Martin, A. Balatsky, T. Wehling, A. Akhmerov, E. Heller and A. Fetter for discussions.

Author information

Author notes

    • Kenjiro K. Gomes
    • , Warren Mar
    •  & Wonhee Ko

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics, Stanford University, Stanford, California 94305, USA

    • Kenjiro K. Gomes
    •  & Hari C. Manoharan
  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

    • Kenjiro K. Gomes
    • , Warren Mar
    • , Wonhee Ko
    •  & Hari C. Manoharan
  3. Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA

    • Warren Mar
  4. Department of Applied Physics, Stanford University, Stanford, California 94305, USA

    • Wonhee Ko
  5. Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, E-28049 Madrid, Spain

    • Francisco Guinea

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Contributions

K.K.G., W.M. and W.K. designed and performed experiments, analysed data and wrote the manuscript. F.G. provided the theoretical analysis. H.C.M. directed the project and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Hari C. Manoharan.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains Supplementary Text and Data, Supplementary Legend for Supplementary Movie 1, Supplementary References and Supplementary Figures 1-4. Supplementary Figure 1 shows a Graphical summary of this work; Supplementary Figure 2 shows the measurement of the surface-state density of states; Supplementary Figure 3 shows the artificial triangular lattice and Supplementary Figure 4 shows the uniaxial strain of graphene lattice.

Videos

  1. 1.

    Supplementary Movie

    This movie shows the nanoscale assembly sequence of an electronic honeycomb lattice by manipulating individual CO molecules on the Cu(111) two-dimensional electron surface state with the STM tip.

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DOI

https://doi.org/10.1038/nature10941

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