Imaging tunable quantum Hall broken-symmetry orders in graphene

When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy(1-5). 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 orders(6-11). Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy(12) or by dielectric screening of the Coulomb interaction(13). However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders(14). 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 Kekule bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz-Thouless transition(15,16). Under dielectric screening, a sublattice-unpolarized ground state(13) emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekule and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions(6-10). This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

Automated summary

In this study, three distinct broken-symmetry phases in graphene were directly imaged using scanning tunnelling spectroscopy. It was found that graphene exhibits different lattice-scale orders under different conditions, deviating from current theoretical predictions. These findings are important for uncovering correlated phases of matter in other quantum materials.