Imaging chiral symmetry breaking from Kekulé bond order in graphene

Abstract

Chirality—or ‘handedness’—is a symmetry property crucial to fields as diverse as biology, chemistry and high-energy physics. In graphene, chiral symmetry emerges naturally as a consequence of the carbon honeycomb lattice. This symmetry can be broken by interactions that couple electrons with opposite momenta in graphene. Here we directly visualize the formation of Kekulé bond order, one such phase of broken chiral symmetry, in an ultraflat graphene sheet grown epitaxially on a copper substrate. We show that its origin lies in the interactions between individual vacancies in the copper substrate that are mediated electronically by the graphene. We show that this interaction causes the bonds in graphene to distort, creating a phase with broken chiral symmetry. The Kekulé ordering is robust at ambient temperature and atmospheric conditions, indicating that intercalated atoms may be harnessed to drive graphene and other two-dimensional materials towards electronically desirable and exotic collective phases.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Adatom-induced Kekulé distortion (KD) in graphene.
Figure 2: Visualizing the Kekulé distortion in graphene.
Figure 3: Mechanism of hidden Kekulé order.
Figure 4: Relating adatom and graphene Kekulé order.
Figure 5: Relationship between the copper substrate and graphene.
Figure 6: Formation of hidden Kekulé order at high temperature.

References

  1. 1

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

    ADS  Article  Google Scholar 

  2. 2

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

    ADS  Article  Google Scholar 

  3. 3

    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 

  4. 4

    Weeks, C. & Franz, M. Interaction-driven instabilities of a Dirac semimetal. Phys. Rev. B 81, 085105 (2010).

    ADS  Article  Google Scholar 

  5. 5

    García-Martínez, N. A., Grushin, A. G., Neupert, T., Valenzuela, B. & Castro, E. V. Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization. Phys. Rev. B 88, 245123 (2013).

    ADS  Article  Google Scholar 

  6. 6

    Cheianov, V. V., Fal’ko, V. I., Syljuåsen, O. & Altshuler, B. L. Hidden Kekulé ordering of adatoms on graphene. Solid State Commun. 149, 1499–1501 (2009).

    ADS  Article  Google Scholar 

  7. 7

    Cheianov, V. V., Syljuåsen, O., Altshuler, B. L. & Fal’ko, V. Ordered states of adatoms on graphene. Phys. Rev. B 80, 233409 (2009).

    ADS  Article  Google Scholar 

  8. 8

    Kopylov, S., Cheianov, V., Altshuler, B. L. & Fal’ko, V. I. Transport anomaly at the ordering transition for adatoms on graphene. Phys. Rev. B 83, 201401 (2011).

    ADS  Article  Google Scholar 

  9. 9

    Chamon, C. Solitons in carbon nanotubes. Phys. Rev. B 62, 2806–2812 (2000).

    ADS  Article  Google Scholar 

  10. 10

    Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).

    ADS  Article  Google Scholar 

  11. 11

    Nambu, Y. & Jona-Lasinio, G. Dynamical model of elementary particles based on an analogy with superconductivity. I. Phys. Rev. 122, 345–358 (1961).

    ADS  Article  Google Scholar 

  12. 12

    Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

    ADS  Article  Google Scholar 

  13. 13

    Hou, C.-Y., Chamon, C. & Mudry, C. Deconfined fractional electric charges in graphene at high magnetic fields. Phys. Rev. B 81, 075427 (2010).

    ADS  Article  Google Scholar 

  14. 14

    Checkelsky, J. G., Li, L. & Ong, N. P. Zero-energy state in graphene in a high magnetic field. Phys. Rev. Lett. 100, 206801 (2008).

    ADS  Article  Google Scholar 

  15. 15

    Marianetti, C. A. & Yevick, H. G. Failure mechanisms of graphene under tension. Phys. Rev. Lett. 105, 245502 (2010).

    ADS  Article  Google Scholar 

  16. 16

    Brown, L. et al. Polycrystalline graphene with single crystalline electronic structure. Nano Lett. 14, 5706–5711 (2014).

    ADS  Article  Google Scholar 

  17. 17

    Gao, L., Guest, J. R. & Guisinger, N. P. Epitaxial graphene on Cu(111). Nano Lett. 10, 3512–3516 (2010).

    ADS  Article  Google Scholar 

  18. 18

    Zhao, L. et al. Influence of copper crystal surface on the CVD growth of large area monolayer graphene. Solid State Commun. 151, 509–513 (2011).

    ADS  Article  Google Scholar 

  19. 19

    Coraux, J., N’Diaye, A. T., Busse, C. & Michely, T. Structural coherency of graphene on Ir(111). Nano Lett. 8, 565–570 (2008).

    ADS  Article  Google Scholar 

  20. 20

    Arguello, C. J. et al. Visualizing the charge density wave transition in 2H-NbSe2 in real space. Phys. Rev. B 89, 235115 (2014).

    ADS  Article  Google Scholar 

  21. 21

    Ruffieux, P. et al. Charge-density oscillation on graphite induced by the interference of electron waves. Phys. Rev. B 71, 153403 (2005).

    ADS  Article  Google Scholar 

  22. 22

    Rutter, G. M. et al. Scattering and interference in epitaxial graphene. Science 317, 219–222 (2007).

    ADS  Article  Google Scholar 

  23. 23

    Deshpande, A., Bao, W., Miao, F., Lau, C. N. & LeRoy, B. J. Spatially resolved spectroscopy of monolayer graphene on SiO2 . Phys. Rev. B 79, 205411 (2009).

    ADS  Article  Google Scholar 

  24. 24

    Mallet, P. et al. Role of pseudospin in quasiparticle interferences in epitaxial graphene probed by high-resolution scanning tunneling microscopy. Phys. Rev. B 86, 045444 (2012).

    ADS  Article  Google Scholar 

  25. 25

    Song, C.-L. et al. Charge-transfer-induced cesium superlattices on graphene. Phys. Rev. Lett. 108, 156803 (2012).

    ADS  Article  Google Scholar 

  26. 26

    Schmid, M. & Varga, P. in The Chemical Physics of Solid Surfaces Vol. 10 (ed. Woodruff, D. P.) 118–151 (Elsevier, 2002).

    Google Scholar 

  27. 27

    Starodub, E. et al. Graphene growth by metal etching on Ru (0001). Phys. Rev. B 80, 235422 (2009).

    ADS  Article  Google Scholar 

  28. 28

    Günther, C., Vrijmoeth, J., Hwang, R. Q. & Behm, R. J. Strain relaxation at hexagonally close-packed metal–metal interfaces. Phys. Rev. Lett. 74, 754–757 (1995).

    ADS  Article  Google Scholar 

  29. 29

    Hamilton, J. C. & Foiles, S. M. Misfit dislocation structure for close-packed metal–metal interfaces. Phys. Rev. Lett. 75, 882–885 (1995).

    ADS  Article  Google Scholar 

  30. 30

    Shao, S., Wang, J., Misra, A. & Hoagland, R. G. Spiral patterns of dislocations at nodes in (111) semi-coherent FCC interfaces. Sci. Rep. 3, 2448 (2013).

    ADS  Article  Google Scholar 

  31. 31

    Zhao, L. et al. Visualizing individual nitrogen dopants in monolayer graphene. Science 333, 999–1003 (2011).

    ADS  Article  Google Scholar 

  32. 32

    Brar, V. W. et al. Gate-controlled ionization and screening of cobalt adatoms on a graphene surface. Nature Phys. 7, 43–47 (2011).

    ADS  Article  Google Scholar 

  33. 33

    Otero, G. et al. Ordered vacancy network induced by the growth of epitaxial graphene on Pt(111). Phys. Rev. Lett. 105, 216102 (2010).

    ADS  Article  Google Scholar 

  34. 34

    Meunier, I., Tréglia, G., Gay, J.-M., Aufray, B. & Legrand, B. Ag/Cu(111) structure revisited through an extended mechanism for stress relaxation. Phys. Rev. B 59, 10910–10917 (1999).

    ADS  Article  Google Scholar 

  35. 35

    van Gastel, R., Somfai, E., van Albada, S. B., van Saarloos, W. & Frenken, J. W. Nothing moves a surface: vacancy mediated surface diffusion. Phys. Rev. Lett. 86, 1562–1565 (2001).

    ADS  Article  Google Scholar 

  36. 36

    Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotech. 5, 722–726 (2010).

    ADS  Article  Google Scholar 

  37. 37

    Stöhr, J. NEXAFS Spectroscopy Vol. 25 (Springer Science & Business Media, 2013).

    Google Scholar 

  38. 38

    Brühwiler, P. A. et al. π and σ excitons in C 1s absorption of graphite. Phys. Rev. Lett. 74, 614–617 (1995).

    ADS  Article  Google Scholar 

  39. 39

    Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  40. 40

    Tersoff, J. & Hamann, D. Theory and application for the scanning tunneling microscope. Phys. Rev. Lett. 50, 1998–2001 (1983).

    ADS  Article  Google Scholar 

  41. 41

    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    ADS  Article  Google Scholar 

  42. 42

    Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Model. Simul. Mater. Sci. Eng. 18, 015012 (2010).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank G. W. Flynn, C. Marianetti, I. L. Aleiner, B. L. Altshuler and C. J. Arguello for helpful discussions and L. Zhao for sharing Gr-Cu(111) bulk crystal data. This work is supported by the Office of Naval Research (ONR) (award number N00014-14-1-0501, C.G.) and by the Air Force Office of Scientific Research (AFOSR) (award number FA9550-11-1-0010, A.N.P.). Work at Cornell University is supported by the NSF through the Cornell Center for Materials Research (NSF DMR-1120296) (J.P.). Support for synthesis and characterization was provided by ONR (N00014-12-1-0791) (K.M.S.), AFOSR (FA9550-11-1-0033 and FA2386-13-1-4118) (J.P.) and the Nano Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (2012M3A7B4049887) (J.P.). NEXAFS data was measured at beamline 8-2 at the Stanford Synchrotron Radiation Lightsource, a National User Facility operated by Stanford University on behalf of the US Department of Energy, Office of Basic Energy Sciences (T.S., D.N.) and supported (T.S.) by the NSF MRSEC Program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634).

Author information

Affiliations

Authors

Contributions

C.G. measured and analysed STM and Raman spectroscopy data and performed DFT and molecular statics calculations. C.-J.K., L.B., and E.B.L. performed CVD growth of graphene samples. J.P. and K.M.S. supervised the CVD sample growth. A.N.P. supervised STM measurements. T.S. and D.N. measured and analysed NEXAFS data. All authors participated in writing the manuscript.

Corresponding author

Correspondence to Abhay N. Pasupathy.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 7492 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gutiérrez, C., Kim, C., Brown, L. et al. Imaging chiral symmetry breaking from Kekulé bond order in graphene. Nature Phys 12, 950–958 (2016). https://doi.org/10.1038/nphys3776

Download citation

Further reading