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-space maps of the conductance as a function of tip position at integer (, 2, 3, 4, 6, 8) and fractional (, , , ) 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. The macroscopic quantization of the Hall resistance measured experimentally in a nonlocal contact configuration survives in the presence of these inhomogeneities, and the relevant local energy scale for the state turns out to be independent of tip position.
- Received 19 September 2013
DOI:https://doi.org/10.1103/PhysRevX.4.011014
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Published by the American Physical Society
Popular Summary
The integer and fractional quantum Hall (QH) effects emerge when a sample containing a two-dimensional electron gas (2DEG) at a low temperature is subjected to a strong magnetic field perpendicular to the plane of the 2DEG. Transport of electrons, either in their natural form (as in the integer QH case) or in the form of fractionally charged quasiparticles (as in the fractional QH case), separates into pairs of two-lane countermoving traffic in a direction given by the magnetic field: one lane along one edge of the sample, the other along the opposite edge. Although the phenomenology has long been known, experimental investigations of the details of those edge transport channels have been rather limited, in particular, in terms of spatial resolution. In this experimental paper, we report a large set of state-of-the-art transport measurements that expand our knowledge of the edge channels.
We measure the conductance of a quantum point contact while the voltage biased tip of a cryogenic scanning probe microscope induces an electron-depleted region in the 2DEG underneath. At finite magnetic field and suitable integer QH states in the bulk of the sample, we find a sequence of lens-shaped regions in the maps of conductance as a function of tip position, which resemble theoretically predicted compressible and incompressible stripes of QH edge states. We have observed a ruggedness on the scale of a few hundred nanometers in the stripes that was not known before. This demonstrates that microscopic inhomogeneities are relevant even in high-quality samples and lead to locally strongly fluctuating widths of incompressible regions, both of the integer and of the fractional QH effect, even down to their complete suppression for certain tip positions. Nevertheless, the macroscopic quantization of the Hall resistance, which is experimentally measured in a nonlocal contact configuration, survives, and the relevant local energy scales turn out to be independent of tip position for integer quantum Hall edge states.
Future experiments employing the same measurement technique, conducted at even lower temperatures, higher magnetic fields, and with even cleaner samples might provide even deeper insights into the peculiar nature of the underlying physics and possible applications in topological quantum computation.