Measuring the berry phase of graphene from wavefront dislocations in friedel oscillations

ABSTRACT Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore crucial for technological

applications. Although the spectral distribution in energy bands is routinely measured by various techniques1, it is more difficult to access the topological properties of band structures

such as the quantized Berry phase, _γ_, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle2. In graphene, the quantized Berry phase _γ_ = π

accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. It is usually thought that measuring the Berry phase requires the

application of external electromagnetic fields to force the charged particles along closed trajectories3. Contradicting this belief, here we demonstrate that the Berry phase of graphene can

be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge density _ρ_ (Friedel oscillations) that are formed at hydrogen atoms

chemisorbed on graphene. Following Nye and Berry6 in describing these topological defects as phase singularities of complex fields, we show that the number of additional wavefronts in the

dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be determined from Friedel oscillations7, our study establishes the

charge density as a powerful observable with which to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study

of the band-structure topology of relativistic and gapped phases in solids. Access through your institution Buy or subscribe This is a preview of subscription content, access via your

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subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS OBSERVATION OF FLOQUET STATES IN GRAPHENE Article Open access 06 May 2025 OBSERVATION OF

FLOQUET–BLOCH STATES IN MONOLAYER GRAPHENE Article 01 May 2025 PROBING THE TUNABLE MULTI-CONE BAND STRUCTURE IN BERNAL BILAYER GRAPHENE Article Open access 11 April 2024 DATA AVAILABILITY

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ACKNOWLEDGEMENTS We thank P. Mallet, J.-Y. Veuillen and J. M. Gómez Rodriguez for experimental support. H.G.-H. and I.B. were supported by AEI and FEDER under project MAT2016-80907-P

(AEI/FEDER, UE), by the Fundación Ramón Areces and by the Comunidad de Madrid NMAT2D-CM programme under grant S2018/NMT-4511. M.I.K. acknowledges the support of NWO via the Spinoza Prize.

AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Laboratoire Ondes et Matière d’Aquitaine, Université de Bordeaux, CNRS UMR 5798, Talence, France C. Dutreix * Departamento de Física de la

Materia Condensada, Universidad Autónoma de Madrid, Madrid, Spain H. González-Herrero & I. Brihuega * Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid,

Spain H. González-Herrero & I. Brihuega * Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, Spain I. Brihuega * Institute for Molecules and Materials, Radboud

University, Nijmegen, The Netherlands M. I. Katsnelson * Université Grenoble Alpes, CEA, IRIG, PHELIQS, Grenoble, France C. Chapelier & V. T. Renard Authors * C. Dutreix View author

publications You can also search for this author inPubMed Google Scholar * H. González-Herrero View author publications You can also search for this author inPubMed Google Scholar * I.

Brihuega View author publications You can also search for this author inPubMed Google Scholar * M. I. Katsnelson View author publications You can also search for this author inPubMed Google

Scholar * C. Chapelier View author publications You can also search for this author inPubMed Google Scholar * V. T. Renard View author publications You can also search for this author

inPubMed Google Scholar CONTRIBUTIONS H.G.-H. and I.B. performed the experiments. V.T.R. discovered the dislocations, which were explained with the theory derived by C.D. M.I.K. and C.C.

gave technical support and conceptual advice. C.D. and V.T.R. wrote the manuscript with the input of all authors. V.T.R. coordinated the collaboration. CORRESPONDING AUTHORS Correspondence

to C. Dutreix or V. T. Renard. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral

with regard to jurisdictional claims in published maps and institutional affiliations. PEER REVIEW INFORMATION _Nature_ thanks An-Ping Li and the other, anonymous, reviewer(s) for their

contribution to the peer review of this work. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION This file contains Supplementary Figures S1 to S10 VIDEO 1: LOCKING OF PSEUDOSPIN ROTATION

ON STM TIP POSITION. This video illustrates the pseudospin rotation in intervalley back-scattering and its winding as the STM tip circles around a H adatom. The STM tip is symbolized by the

purple dot. Momentums are symbolized by grey arrows, the pseudospin of the incident electron in valley K is symbolized by a blue arrow and the pseudospin of the reflected electron in the K´

valley is symbolized by a red arrow. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Dutreix, C., González-Herrero, H., Brihuega, I. _et al._ Measuring

the Berry phase of graphene from wavefront dislocations in Friedel oscillations. _Nature_ 574, 219–222 (2019). https://doi.org/10.1038/s41586-019-1613-5 Download citation * Received: 07

January 2019 * Accepted: 16 July 2019 * Published: 30 September 2019 * Issue Date: 10 October 2019 * DOI: https://doi.org/10.1038/s41586-019-1613-5 SHARE THIS ARTICLE Anyone you share the

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