Absence of edge reconstruction for quantum Hall edge channels in graphene devices.

Quantum Hall (QH) edge channels propagating along the periphery of two-dimensional (2D) electron gases under perpendicular magnetic field are a major paradigm in physics. However, groundbreaking experiments that could use them in graphene are hampered by the conjecture that QH edge channels undergo a reconstruction with additional nontopological upstream modes. By performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride, we show that QH edge channels are confined to a few magnetic lengths at the crystal edges. This implies that they are ideal 1D chiral channels defined by boundary conditions of vanishing electronic wave functions at the crystal edges, hence free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, incompatible with the existence of upstream modes. This work has profound implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

Imaging tunable quantum Hall broken-symmetry orders in graphene.

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.

Helical quantum Hall phase in graphene on SrTiO3.

The ground state of charge-neutral graphene under perpendicular magnetic field was predicted to be a quantum Hall topological insulator with a ferromagnetic order and spin-filtered, helical edge channels. In most experiments, however, an insulating state is observed that is accounted for by lattice-scale interactions that promote a broken-symmetry state with gapped bulk and edge excitations. We tuned the ground state of the graphene zeroth Landau level to the topological phase through a suitable screening of the Coulomb interaction with the high dielectric constant of a strontium titanate (SrTiO3) substrate. Robust helical edge transport emerged at magnetic fields as low as 1 tesla and withstanding temperatures up to 110 kelvin over micron-long distances. This versatile graphene platform may find applications in spintronics and topological quantum computation.