Scanning capacitive studies in the Quantum Hall regime

This research has been focused on studies of the two-dimensional (2D) electron gas in the quantum Hall regime using a novel scanning capacitive microscopy. In particular, I have performed imaging of the incompressible strips in the quantum Hall regime and have measured the random potential inside a 2D electron gas by scanning an in situ formed quantum dot. Details about these two projects are otlined below.

2.5x2.5 microns topographic map of random
potential in the integer quantum Hall fluid
measured by single electrons additions to a 
scannable mobile quantum dot.
See slides from my Nov. 2001 talk at the 
Institute of Theoretical Physics, UCSB.
Measuring random potential by a Mobile Quantum Dot:
By applying a voltage between the scanning tip and the sample we locally enhance the density of the 2D electrons underneath the tip. At high magnetic fields, we thereby create a droplet of electrons on the next Landau level. An incompressible strip with an integer number of filled Landau level surrounds the droplet and serves as a tunneling barrier. The number of electrons in the droplet becomes quantized and it exhibits a Coulomb blockade. The droplet follows the tip position as we scan the tip across the sample. We therefore may call it a Mobile Quantum Dot. Unlike the more conventionally studied quantum dots, the mobile quantum dot is formed inside the 2D electron gas without lithographic patterning of the semiconductor. The dot serves as an in situ detector of the random electrostatic potential inside the 2D electron gas. Namely, we scan the dot across the sample and measure the changes in the number of electrons in the dot induced by the random potential.
Topographic Mapping of the Quantum Hall Liquid Using a Few-Electron Bubble.
G. Finkelstein, P.I. Glicofridis, R.C. Ashoori and M. Shayegan,
Science 289, p. 90 (2000).

Imaging of low compressibility strips in the quantum Hall liquid:
The “incompressible strips” formed near the Hall bar edges play an important role in the physics of the quantum Hall effect . Within an incompressible strip, the 2D electron density is constant, so that an exactly integer number of Landau levels is filled. As a result, the Fermi energy lies inside the cyclotron gap of the density of states and the electron gas compressibility is zero. Using scanning capacitive microscopy we have imaged in detail the strips corresponding to several integer quantum Hall filling factors. We have focused on two properties of the strips: the local density of states and electric resistivity across the strip. Contrary to the term “incompressible”, we have found that in the moderate quality samples the 2D electron gas inside the strips has a nonzero density of states. The measured widths of the strips turn out to be significantly wider than predicted by theory. We have explained the broadening of the strips by considering a disorder-induced nonzero density of states in the cyclotron gap. Our conclusion has been supported by theoretical considerations. We also have found that electrical resistivity of across the strips may vary by orders of magnitude. Interestingly, when the strips move to a region of higher density gradient, where they are expected to become narrower, their resistivity steadily grows.
Imaging of Low- Compressibility Strips in the Quantum Hall Liquid.
G. Finkelstein, P.I. Glicofridis, S.H. Tessmer, R.C. Ashoori and M. R. Melloch,
Physical Review B 61, p. R16323 (2000).

Determination of the Resistance across Incompressible Strips through Imaging of Charge Motion.
P.I. Glicofridis, G. Finkelstein, R.C. Ashoori and M. Shayegan,
Physical Review B 65, p. R121312 (2002).