Like restless children posing for a family portrait, electrons won’t hold
still long enough to stay in any kind of fixed arrangement.
Now, a Cornell-led collaboration has developed a way to stack
two-dimensional semiconductors and trap electrons in a repeating pattern
that forms a specific and long-hypothesized crystal.
The team’s paper, “Correlated Insulating States at Fractional Fillings of
Moiré Superlattices,” published Nov. 11 in Nature. The paper’s lead author
is postdoctoral researcher Yang Xu.
The project grew out of the shared lab of Kin Fai Mak, associate professor
of physics in the College of Arts and Sciences, and Jie Shan, professor of
applied and engineering physics in the College of Engineering, the paper’s
co-senior authors. Both researchers are members of the Kavli Institute at
Cornell for Nanoscale Science; they came to Cornell through the provost’s
Nanoscale Science and Microsystems Engineering (NEXT Nano) initiative.
A crystal of electrons was first predicted in 1934 by theoretical physicist
Eugene Wigner. He proposed that when the repulsion that results from
negatively charged electrons – called Coulomb repulsions – dominates the
electrons’ kinetic energy, a crystal would form. Scientists have tried
various methods to suppress that kinetic energy, such as putting electrons
under an extremely large magnetic field, roughly a million times that of the
Earth’s magnetic field. Complete crystallization remains elusive, but the
Cornell team discovered a new method for achieving it.
“Electrons are quantum mechanical. Even if you don’t do anything to them,
they’re spontaneously jiggling around all the time,” Mak said. “A crystal of
electrons would actually have the tendency to just melt because it’s so hard
to keep the electrons fixed at a periodic pattern.”
So the researchers’ solution was to build an actual trap by stacking two
semiconductor monolayers, tungsten disulfide (WS2) and tungsten diselenide
(WSe2), grown by partners at Columbia University. Each monolayer has a
slightly different lattice constant. When paired together, they create a
moiré superlattice structure, which essentially looks like a hexagonal grid.
The researchers then placed electrons in specific sites in the pattern. As
they found in an earlier project, the energy barrier between the sites locks
the electrons in place.
“We can control the average occupancy of the electrons at a specific moiré
site,” Mak said.
Given the intricate pattern of a moiré superlattice, combined with the
jittery nature of electrons and the need to put them into a very specific
arrangement, the researchers turned to Veit Elser, professor of physics and
a co-author of the paper, who calculated the ratio of occupancy by which
different arrangements of electrons will self-crystallize.
However, the challenge of Wigner crystals is not only creating them, but
observing them, too.
“You need to hit just the right conditions to create an electron crystal,
and at the same time, they’re also fragile,” Mak said. “You need a good way
to probe them. You don’t really want to perturb them significantly while
probing them.”
The team devised a new optical sensing technique in which an optical sensor
is placed close to the sample, and the whole structure is sandwiched between
insulating layers of hexagonal boron nitride, created by collaborators at
the National Institute for Materials Science in Japan. Because the sensor is
separated from the sample by about two nanometers, it doesn’t perturb the
system.
The new technique enabled the team to observe numerous electron crystals
with different crystal symmetries, from triangular-lattice Wigner crystals
to crystals that self-aligned into stripes and dimers. By doing so, the team
demonstrated how very simple ingredients can form complex patterns – as long
as the ingredients sit still long enough.
Reference:
Xu, Y., Liu, S., Rhodes, D.A. et al. Correlated insulating states at
fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).
https://doi.org/10.1038/s41586-020-2868-6
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