Imaging tunable quantum Hall broken-symmetry orders in graphene

Abstract

Charge-neutral graphene under perpendicular magnetic field was predicted to harbor a rich variety of many-body ground states with distinct topological and symmetry breaking orders. We directly image the atomic-scale electronic wavefunction of three distinct broken-symmetry phases in graphene using scanning tunneling spectroscopy. We explore the phase diagram by controllably tuning the magnetic field and the screening of the Coulomb interaction by close proximity to a low or high dielectric constant substrate. In the unscreened case, we unveil a Kekulé bond order. Under dielectric screening, a sublattice-unpolarized ground state emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. In both cases we further observed the coexistence of additional, secondary lattice-scale orders. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride

“…21,33 . However, more recently, scanning tunneling spectroscopy (STS) meaurements have in fact detected a transition from the CDW states to a KD state at neutrality 34,35 , and therefore these experiments have a great potential to detect the corresponding transition in the fractionally filled case that we predict here.…”

“…This is why we have termed this state a "CaKD" (Canted Kekule Distortion) to emphasize this difference from the KD state at neutrality where the two occupied spinors have a common orientation in the valley Bloch sphere and thus a valley ferromagnetic-like character. Recent tunneling experiments have demonstrated clear and tantalizing evidence for the presence of these states 34,35 .…”

“…The quantum Hall regime in Graphene offers a fantastic arena to investigate the interplay of broken symmetry, topology and fractionalization , that continues to flourish thanks to a combination of high quality samples, enlarged degeneracy from its valley degree of freedom, and its exposed nature that allows new ways to measure and control the states of interest. For example, recent experiments have developed remarkable techniques to generate and detect long-range transmission of collective excitations in broken-symmetry integer and fractional quantum Hall states 7,21,22,[28][29][30][31][32][33][34] , and recent scanning tunneling microscopy has provided detailed evidence of valence-bond quantum Hall Kekule-type states 34,35 .…”

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

“…On the other hand, 1e-skyrmions are tightly localized within a few moiré lengths and give rise to a spatially varying KD when pinned by charged impurities. KD has been observed in the related context of QHFM within the lowest LL of monolayer graphene [103][104][105] , including the imaging of an individual valley skyrmion 104 . We caution that KD in TBG has also been predicted for IKS order in the presence of a small amount of strain 20,102 .…”

Spectroscopy of Twisted Bilayer Graphene Correlated Insulators

“…the modulation of the STM signal at wavevectors connecting the two graphene valleys) -together with the knowledge of their Chern number, can distinguish among the candidate many-body states. The ability to use the STM to directly visualize broken symmetry states, including valley-polarized or Kekule order due to many-body interactions in a low-density flat band system, has recently been demonstrated in probing such states forming in the zeroth Landau level of monolayer graphene [78][79][80]. These findings and the techniques developed for directly measuring the order parameters of various phases using local phase-sensitive analysis of Fourier-transformed STM conductance maps can also be used to verify the nature of many-body ground states we examine here for TBG.…”