Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

Abstract

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $${{\nu }}={{0}},\pm {{1}}$$ ν = 0 , ± 1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

“…We find that tip-induced band bending is negligible in most of our measurements, which likely contributes to our ability to observe symmetrybreaking gaps. While we occasionally find tips that show signature of band bending in spectroscopic measurements (26) similar to previous studies (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38), data sets we obtained with improved tip conditions demonstrate the following differences. First, our data as shown in Fig.…”

Measuring and Tuning the Potential Landscape of Electrostatically Defined Quantum Dots in Graphene

“…In a KPFM measurement, the local contact potential difference (LCPD) between the surface of a material and the conductive tip of an atomic force microscope (AFM) is spatially mapped across the sample . For graphene, KPFM measurements have been used to characterize several phenomena: the dependence of work function on carrier density, Moirè pattern potentials, quantum Hall edge states, screening clouds near defects, potential drops across biased samples, , and near electrical contacts . One complication of KPFM measurements is that the tip can have both a sharp (∼10 nm) apex and a large (∼1–10 μm) body which can measure different short- and long-range, respectively, CPD values .…”

Energy Dissipation from Confined States in Nanoporous Molecular Networks

“…We foresee that AFM spectroscopy will not only allow the local gating of artificial lattices on metals but also induce a quantum phase transition in dual-gated heterostructure devices where a back-gate voltage can be additionally applied. 37 EXPERIMENTAL SECTION Molecule Synthesis. 2,7-Dihydroxypyrene (DHP) was prepared according to literature procedures.…”