Researchers trap electrons to create elusive crystal

Like restless children posing for a family portrait, electrons will not stay still long enough to stay in any kind of fixed arrangement.

Cornell researchers stacked two-dimensional semiconductors to create a moiré superlattice structure that traps electrons in a repeating pattern, ultimately forming the long-assumed Wigner crystal.

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, long-held, hypothetical crystal.

The team’s document, “Correlated Insulating States at Fractional Fillings of Moiré Superlattices”, published on November 11 in Nature. The main author of the article is postdoctoral researcher Yang Xu.

The project originated from the shared lab of Kin Fai Mak, associate professor of physics at the College of Arts and Sciences, and Jie Shan, professor of applied physics and engineering at the College of Engineering, co-lead authors of the article. Both researchers are members of the Cornell Kavli Institute for Nanoscale Science; they came to Cornell as part of the provost’s Nanoscale Science and Microsystems Engineering (NEXT Nano) initiative.

An electron crystal was first predicted in 1934 by theoretical physicist Eugene Wigner. He proposed that when the resulting repulsion of negatively charged electrons – called Coulomb repulsions – dominated the kinetic energy of the electrons, a crystal would form. Scientists have tried various methods to suppress this kinetic energy, such as placing electrons under an extremely large magnetic field, about a million times that of Earth’s magnetic field. Complete crystallization remains elusive, but the Cornell team have discovered a new method to achieve it.

“Electrons are quantum mechanics. Even if you don’t do anything to them, they spontaneously move all the time,” Mak said. “An electron crystal would actually tend to just melt because it’s so difficult to keep electrons attached to a periodic pattern.”

The researchers’ solution was therefore to build a real trap by stacking two monolayers of semiconductors, 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 basically looks like a hexagonal grid. The researchers then placed electrons in specific sites of the motif. As they discovered in a previous project, the energy barrier between the sites locks the electrons in place.

“We can monitor the average electron occupancy at a specific moiré site,” Mak said.

Given the complex model of a moire superlattice, combined with the nerve nature of electrons and the need to place them in a very specific arrangement, the researchers turned to Veit Elser, professor of physics and co-author of the article, which calculated the occupancy ratio according to which the different arrangements of electrons will autocrystallize.

However, the challenge of Wigner crystals is not only to create them, but also to observe them.

“You have to achieve the right conditions to create an electron crystal, and at the same time, they are also fragile,” Mak said. “You need a good way to probe them. You don’t really want to significantly disturb them while probing them.”

The team has developed a new optical detection technique in which an optical sensor is placed near the sample and the entire structure is sandwiched between insulating layers of hexagonal boron nitride, created by collaborators at the ‘National Institute of Materials Science in Japan. As the sensor is separated from the sample by approximately two nanometers, it does not interfere with the system.

The new technique allowed the team to observe numerous electron crystals with different crystal symmetries, from triangular lattice Wigner crystals to crystals that self-align in stripes and dimers. In doing so, the team demonstrated how very simple ingredients can form complex patterns, provided the ingredients remain long enough.