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Imaging the Conductance of Integer and Fractional Quantum Hall Edge States

N. Pascher,C. Rossler,T. Ihn,K. Ensslin,C. Reichl,W. Wegscheider

Published 2013 in Physical Review X

ABSTRACT

We measure the conductance of a quantum point contact while the biased tip of a scanning probe microscope induces a depleted region in the electron gas underneath. At a finite magnetic field, we find plateaus in the real-spacemaps of the conductance as afunction of tip position atinteger(ν ¼ 1,2,3,4,6,8) and fractional (ν ¼ 1=3, 2=3, 5=3, 4=5) values of transmission. They resemble theoretically predicted compressible and incompressible stripes of quantum Hall edge states. The scanning tip allows us to shift the constriction limiting the conductance in real space over distances of many microns. The resulting stripes of integer and fractional filling factors are rugged on scales of a few hundred nanometers, i.e., on a scale much smaller than the zero-field elastic mean free path of the electrons. Our experiments demonstrate that microscopic inhomogeneities are relevant even in high-quality samples and lead to locally strongly fluctuating widths of incompressible regions even down to their complete suppression for certain tip positions.ThemacroscopicquantizationoftheHallresistancemeasuredexperimentallyinanonlocalcontact configuration survives in the presence of these inhomogeneities, and the relevant local energy scale for the ν ¼ 2 state turns out to be independent of tip position.

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