Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Designer Dirac fermions and topological phases in molecular graphene

Nature volume 483, pages 306–310 (2012)Cite this article

Subjects

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

Rent or Buy

All prices are NET prices.

Figure 1: Dirac fermions in molecular graphene.
Figure 2: Dirac point engineering in a p–n–p junction.
Figure 3: Charge- and bond-density waves in molecular graphene.
Figure 4: Landau quantization and topological zero modes in a tunable pseudomagnetic field.

References

  1. 1

    Castro Neto, A., Guinea, F., Peres, N., Novoselov, K. & Geim, A. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)

    ADS  CAS  Article  Google Scholar 

  2. 2

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

    ADS  CAS  Article  Google Scholar 

  3. 3

    Zhu, S.-L., Wang, B. & Duan, L.-M. Simulation and detection of Dirac fermions with cold atoms in an optical lattice. Phys. Rev. Lett. 98, 260402 (2007)

    ADS  Article  Google Scholar 

  4. 4

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

    Article  Google Scholar 

  5. 5

    Moon, C. R., Mattos, L. S., Foster, B. K., Zeltzer, G. & Manoharan, H. C. Quantum holographic encoding in a two-dimensional electron gas. Nature Nanotechnol. 4, 167–172 (2009)

    ADS  CAS  Article  Google Scholar 

  6. 6

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

    ADS  Article  Google Scholar 

  7. 7

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

    ADS  Article  Google Scholar 

  8. 8

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

    ADS  Article  Google Scholar 

  9. 9

    Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nature Phys. 6, 30–33 (2010)

    ADS  CAS  Article  Google Scholar 

  10. 10

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

    ADS  CAS  Article  Google Scholar 

  11. 11

    Hou, C.-Y., Chamon, C. & Mudry, C. Electron fractionalization in two-dimensional graphenelike structures. Phys. Rev. Lett. 98, 186809 (2007)

    ADS  Article  Google Scholar 

  12. 12

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

    ADS  CAS  Article  Google Scholar 

  13. 13

    Cahangirov, S., Topsakal, M., Aktürk, E., Şahin, H. & Ciraci, S. Two- and one-dimensional honeycomb structures of silicon and germanium. Phys. Rev. Lett. 102, 236804 (2009)

    ADS  CAS  Article  Google Scholar 

  14. 14

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

    ADS  CAS  Article  Google Scholar 

  15. 15

    Moon, C. R., Lutz, C. P. & Manoharan, H. C. Single-atom gating of quantum-state superpositions. Nature Phys. 4, 454–458 (2008)

    ADS  CAS  Article  Google Scholar 

  16. 16

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

    ADS  MathSciNet  CAS  Article  Google Scholar 

  17. 17

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

    ADS  CAS  Article  Google Scholar 

  18. 18

    Katsnelson, M., Novoselov, K. & Geim, A. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620–625 (2006)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Cheianov, V., Fal’ko, V. & Altshuler, B. The focusing of electron flow and a Veselago lens in graphene p-n junctions. Science 315, 1252–1255 (2007)

    ADS  CAS  Article  Google Scholar 

  20. 20

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

    ADS  Article  Google Scholar 

  21. 21

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

    ADS  Article  Google Scholar 

  22. 22

    Guinea, F., Katsnelson, M. & Vozmediano, M. Midgap states and charge inhomogeneities in corrugated graphene. Phys. Rev. B 77, 075422 (2008)

    ADS  Article  Google Scholar 

  23. 23

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

    ADS  Article  Google Scholar 

  24. 24

    Martin, I., Blanter, Y. & Morpurgo, A. Topological confinement in bilayer graphene. Phys. Rev. Lett. 100, 036804 (2008)

    ADS  Article  Google Scholar 

  25. 25

    Nomura, K., Koshino, M. & Ryu, S. Topological delocalization of two-dimensional massless Dirac fermions. Phys. Rev. Lett. 99, 146806 (2007)

    ADS  Article  Google Scholar 

  26. 26

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

    ADS  Article  Google Scholar 

  27. 27

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

    ADS  CAS  Article  Google Scholar 

  28. 28

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

    ADS  Article  Google Scholar 

  29. 29

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

    ADS  Article  Google Scholar 

  30. 30

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

    ADS  CAS  Article  Google Scholar 

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

  1. Kenjiro K. Gomes, Warren Mar and Wonhee Ko: These authors contributed equally to this work.

Affiliations

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

    Kenjiro K. Gomes & Hari C. Manoharan

  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, 94025, California, USA

    Kenjiro K. Gomes, Warren Mar, Wonhee Ko & Hari C. Manoharan

  3. Department of Electrical Engineering, Stanford University, Stanford, 94305, California, USA

    Warren Mar

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

    Wonhee Ko

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

    Francisco Guinea

Authors
  1. Kenjiro K. Gomes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Warren Mar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wonhee Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Francisco Guinea
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hari C. Manoharan
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Corresponding author

Correspondence to Hari C. Manoharan.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

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. (PDF 3256 kb)

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. (MOV 4353 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gomes, K., Mar, W., Ko, W. et al. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012). https://doi.org/10.1038/nature10941

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing