Scanning capacitive studies in the
Quantum Hall regime
This research has been focused on studies of the twodimensional
(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 FewElectron 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 disorderinduced
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).