Edge Channels of Broken Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy

The quantum Hall effect, a topologically non-trivial quantum phase has brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are the essential features of the QH effect, however microscopic local probe studies of edge states have been conducted with limited success. The QH edge states in graphene are special since they emerge from four-fold nearly-degenerate Landau levels. In this talk, we present a microscopic study a of the QH edge states originating from the broken symmetry states of zeroth LL in graphene using AFM. The KPFM detects the chemical potential transitions when Landau levels are being filled or empty as a function of back gate potential and show the same fidelity for Landau level spectroscopy as STS measurements. In particular broken symmetry states can be resolved at integer filling factors ν=0, ±1 inside the N=0 Landau level manifold, showing the lifting of the graphene four-fold degeneracy due to spin and valley. The edge channels emerging from integer filling factors are spatially mapped across the quantum Hall edge using AFM. The microscopic properties by scanning probe measurement of quantum Hall edge channels can be correlated with macroscopic properties measured with in-situ magnetotransport.