Hexbyte Glen Cove Electrons falling flat: Germanium falls into a 2-D arrangement on zirconium diboride thumbnail

Hexbyte Glen Cove Electrons falling flat: Germanium falls into a 2-D arrangement on zirconium diboride

Hexbyte Glen Cove

Figure 1. Ball-and-stick model for bitriangular Ge lattice on zirconium diboride   Germanium atoms (light and dark blue) spontaneously crystallize into a two-dimensional (2D) “bitriangular” lattice on zirconium diboride thin films grown on germanium single crystals (green: Zr atoms, orange: B atoms). Credit: Japan Advanced Institute of Science and Technology

Scientists have recently revealed, both theoretically and experimentally, that germanium atoms can arrange themselves into a 2-D “bi-triangular” lattice on zirconium diboride thin films grown on germanium single crystals to form a “flat band material” with an embedded “kagome” lattice. The result provides experimental support to a theoretical prediction of flat bands emerging from trivial atomic geometry and indicates the possibility of their existence in many more materials.

The human mind is naturally drawn to objects that possess symmetry; in fact, the notion of beauty is often conflated with symmetry. In nature, nothing epitomizes symmetry more than crystals. Since their discovery, crystals have attracted a great deal of attention not only by their unique “symmetrical” aesthetic appeal but also by their unique properties. One of these properties is the behavior of electrons inside a crystal. From a physical point of view, an electron within a crystal can be fully characterized by its energy and a quantity called “crystal momentum,” which relates to how fast the electron moves in a crystal. The relationship between the energy and crystal momentum of electrons is what scientists refer to as “band ,” which, put simply, is the allowed energy levels for the electrons within the crystal.

Recently, materials scientists have turned their attention towards what are called “flat band materials”—a class of materials possessing a in which the energy does not vary with the crystal momentum and hence resembles a flat line when plotted as a function of crystal momentum—owing to their ability to give rise to exotic states of matter, such as ferromagnetism (iron-like spontaneous magnetism) and superconductivity (zero resistance to electricity flow). Generally, these “flat bands” are observed in special 2-D structures that go by names like “checkerboard ,” “dice lattice,” “kagome lattice,” etc. and are typically observed either within the crystal or at the surface of layered materials. A pertinent question thus presents itself—is it possible to embed such lattices into completely new 2-D structures? Efforts to design 2-D materials have focused on answering this question, and a recent finding suggests that the answer is a “yes.”

Now, in a study published in Physical Review B as a Rapid Communication, an international team of scientists from the Japan Advanced Institute of Science and Technology (JAIST), the University of Tokyo, the Japan Atomic Energy Agency, and Institute for Molecular Science in Japan and Tamkang University in Taiwan, led by Dr. Antoine Fleurence and Prof. Yukiko Yamada-Takamura, has reported a possible new flat band material obtained from germanium (Ge) atoms arranging themselves into a 2-D bi-triangular lattice on zirconium diboride thin films grown on germanium . While the team had already grown this 2-D material years ago, they were only recently able to unveil its structure.

Last year, a part of the team published a theoretical paper in the same journal underlining the conditions under which a 2-D bi-triangular lattice can form a flat band. They found that this is related to a “kagome” (meaning weaved basket pattern in Japanese) lattice—a term originally coined by Japanese physicists in the ’50s to study magnetism. “I was really excited when I found out that the electronic structure of kagome lattice can be embedded into a very different-looking 2-D structure,” recalls Prof. Chi-Cheng Lee, a physicist at Tamkang University, Taiwan, involved in the study, who predicted the presence of flat bands in the “bitriangular” lattice.

The prediction was finally confirmed after the team, in their current study, characterized the prepared 2-D material using various techniques such as scanning tunneling microscopy, positron diffraction, and core-level and angle-resolved photoelectron emission; and backed up the experimental data with theoretical calculations to reveal the underlying bi-triangular lattice.

“The result is really exciting as it shows that flat bands can emerge even from trivial structures and can possibly be realized in many more materials. Our next step is to see what happens at low temperature, and how it is related to the flat bands of the Ge bi-triangular lattice,” says Dr. Fleurence, who is also the first author of this paper.

Indeed, who would’ve thought that a typical, run-of-the-mill semiconductor like germanium could offer such exotic and unprecedented possibilities? The 2-D world might have more surprises up its sleeve than we imagine.



More information:
A. Fleurence et al. Emergence of nearly flat bands through a kagome lattice embedded in an epitaxial two-dimensional Ge layer with a bitriangular structure, Physical Review B (2020). DOI: 10.1103/PhysRevB.102.201102

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Japan Advanced Institute of Science and Technology

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Electrons falling flat: Germanium falls into a 2-D arrangement on zirconium diboride (2020, December 4)
retrieved 4 December 2020
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Hexbyte Glen Cove Researchers trap electrons to create elusive crystal thumbnail

Hexbyte Glen Cove Researchers trap electrons to create elusive crystal

Hexbyte Glen Cove

Credit: Unsplash/CC0 Public Domain

Like restless children posing for a family portrait, electrons won’t hold 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 , ultimately forming the long-hypothesized 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 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 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.



More information:
Yang Xu et al. Correlated insulating states at fractional fillings of moiré superlattices, Nature (2020). DOI: 10.1038/s41586-020-2868-6

Citation:
Researchers trap electrons