Imaging tunable quantum Hall broken-symmetry orders in graphene

Alexis Coissard, David Wander, Hadrien Vignaud, Adolfo G. Grushin, Cécile Repellin, Kenji Watanabe, Takashi Taniguchi, Frédéric Gay, Clemens B. Winkelmann, Hervé Courtois, Hermann Sellier and Benjamin Sacépé ()
Additional contact information
Alexis Coissard: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
David Wander: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Hadrien Vignaud: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Adolfo G. Grushin: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Cécile Repellin: Université Grenoble-Alpes, CNRS, LPMMC
Kenji Watanabe: National Institute for Materials Science
Takashi Taniguchi: National Institute for Materials Science
Frédéric Gay: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Clemens B. Winkelmann: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Hervé Courtois: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Hermann Sellier: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel
Benjamin Sacépé: Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel

Nature, 2022, vol. 605, issue 7908, 51-56

Abstract: Abstarct When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy1–5. The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders6–11. Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy12 or by dielectric screening of the Coulomb interaction13. However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders14. Here we image three distinct broken-symmetry phases in graphene using scanning tunnelling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz–Thouless transition15,16. Under dielectric screening, a sublattice-unpolarized ground state13 emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions6–10. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

Date: 2022
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DOI: 10.1038/s41586-022-04513-7

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