Abstract
The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from how non-relativistic electrons behave in traditional atomic and impurity systems1,2,3. Surprisingly, many key theoretical predictions for this ultra-relativistic regime have not been tested4,5,6,7,8,9,10,11,12. Graphene, a two-dimensional material in which electrons behave like massless Dirac fermions13,14, provides a unique opportunity to test such predictions. Graphene’s response to a Coulomb potential also offers insight into important material characteristics, including graphene’s intrinsic dielectric constant6,8, which is the primary factor determining the strength of electron–electron interactions in graphene15. Here we present a direct measurement of the nanoscale response of Dirac fermions to a single Coulomb potential placed on a gated graphene device. Scanning tunnelling microscopy was used to fabricate tunable charge impurities on graphene, and to image electronic screening around them for a Q = +1|e| charge state. Electron-like and hole-like Dirac fermions were observed to respond differently to a Coulomb potential. Comparing the observed electron–hole asymmetry to theoretical simulations has allowed us to test predictions for how Dirac fermions behave near a Coulomb potential, as well as extract graphene’s intrinsic dielectric constant: ɛg = 3.0±1.0. This small value of ɛg indicates that electron–electron interactions can contribute significantly to graphene properties.
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Acknowledgements
Research supported by the Office of Naval Research Multidisciplinary University Research Initiative award no. N00014-09-1-1066 (graphene device preparation and characterization), by the Director, Office of Science, Office of Basic Energy Sciences of the US Department of Energy under contract no. DE-AC02-05CH11231 (STM instrumentation development and measurements), and by the National Science Foundation award no. DMR-0906539 (numerical simulations).
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Y.W., V.W.B. and M.F.C. designed the experiment and made the measurements. Q.W., W.R., H-Z.T. and A.Z. facilitated the sample fabrication. A.V.S., L.S.L. and Y.W. carried out the theoretical calculation. Y.W., V.W.B., A.V.S., L.S.L. and M.F.C. carried out the analysis and wrote the paper.
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Wang, Y., Brar, V., Shytov, A. et al. Mapping Dirac quasiparticles near a single Coulomb impurity on graphene. Nature Phys 8, 653–657 (2012). https://doi.org/10.1038/nphys2379
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DOI: https://doi.org/10.1038/nphys2379
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