Selected Applications
Scanning Gate Microscopy at 300 mK
In this measurement, an attoAFM III was operated inside an attoLIQUID3000 cryostat at 300 mK in scanning gate microscopy mode (SGM) - investigating the trajectory
and interaction of edge channels of a split-gate quantum point contact (QPC) device
in the Quantum Hall (QH) regime. By scanning the SGM tip over the surface of the QPC
at constant height and by simultaneously measuring and plotting the source-drain
current, conductance maps were obtained. The image to the left is an example of
such a conductance map depicting the characteristic branched-flow of electrons at
zero magnetic field, which in turn shows electron interference fringes and the actual
electron path (T = 400 mK, 2DEG density n2D = 3.37 x 1011 cm-2).
(Data and images were generously provided by S. Heun et al., NEST, CNR-INFM and Scuola Normale Superiore, Pisa,
Italy.)
Imaging Fractional Incompressible Stripes in Integer Quantum
Hall Systems
In newer measurements, the group performed SGM measurements at the temperature
and magnetic field conditions required to observe the fractional quantum Hall effect. The goal is to image for the first time the presence of fractional incompressible
stripes, i.e. the existence of an inner structure within the integer edge channel. The
measurements were performed at bulk filling factor n = 1 (B = 8.23 T, T = 300 mK). The
corresponding SGM map in the region close to the QPC center is depicted in the lower
Figure (a). Analogously to the n = 4 case, one expects to find plateaus when the local
electron phase is gapped, i.e. when the local filling factor n*equals a robust fraction.
The scan profile depicted in the right figure reveals a clear shoulder for Gsd = e2/3h
(corresponding to points where n* = 1/3). A more careful analysis [1] allows to determine the occurrence of incompressible phases for n* = 1/3, 2/5, 2/3, and 3/5, i.e. the
two most robust fractions and their hole-particle conjugates, respectively. The SGM
maps allow not only to reveal the fractional incompressible stripes, but also to measure their width and correlate it with the local electron density slope. The agreement
between the data and a reconstruction model is remarkable, especially in light of the
uncertainty on the fractional-gap value, which is known to be rather sensitive to the
details of disorder potential.
(Data and images were generously provided by N. Paradiso, S. Heun et al., NEST, CNR-INFM and Scuola Normale
Superiore, Pisa, Italy.)
[1] N. Paradiso et al., Phys. Rev. Lett. 108, 246801 (2012). See also the Supplemental Material.
attoMICROSCOPY
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attoAFM III
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