Space is usually considered infinitely divisible — given any two positions, there is always a position halfway between. But in a recent study aimed at developing ultra-fast transistors using graphene, researchers from the UCLA Department of Physics and Astronomy and the California NanoSystems Institute show that dividing space into discrete locations, like a chessboard, may explain how point-like electrons, which have no finite radius, manage to carry their intrinsic angular momentum, or "spin."
While studying graphene's electronic properties, professor Chris Regan and graduate student Matthew Mecklenburg found that a particle can acquire spin by living in a space with two types of positions — dark tiles and light tiles. The particle seems to spin if the tiles are so close together that their separation cannot be detected.
"An electron's spin might arise because space at very small distances is not smooth, but rather segmented, like a chessboard," Regan said.
Their findings are published in the March 18 edition of the journal Physical Review Letters.
In quantum mechanics, "spin up" and "spin down" refer to the two types of states that can be assigned to an electron. That the electron's spin can have only two values — not one, three or an infinite number — helps explain the stability of matter, the nature of the chemical bond and many other fundamental phenomena.
However, it is not clear how the electron manages the rotational motion implied by its spin. If the electron had a radius, the implied surface would have to be moving faster than the speed of light, violating the theory of relativity. And experiments show that the electron does not have a radius; it is thought to be a pure point particle with no surface or substructure that could possibly spin.
In 1928, British physicist Paul Dirac showed that the spin of the electron is intimately related to the structure of space-time. His elegant argument combined quantum mechanics with special relativity, Einstein's theory of space-time (famously represented by the equation E=mc2).
Dirac's equation, far from merely accommodating spin, actually demands it. But while showing that relativistic quantum mechanics requires spin, the equation does not give a mechanical picture explaining how a point particle manages to carry angular momentum, nor why this spin is two-valued.
Unveiling a concept that is at once novel and deceptively simple, Regan and Mecklenburg found that electrons' two-valued spin can arise from having two types of tiles — light and dark — in a chessboard-like space. And they developed this quantum mechanical model while working on the surprisingly practical problem of how to make better transistors out of a new material called graphene.
Graphene, a single sheet of graphite, is an atomically-thin layer of carbon atoms arranged in a honeycomb structure. First isolated in 2004 by Andre Geim and Kostya Novoselov, graphene has a wealth of extraordinary electronic properties, such as high electron mobility and current capacity. In fact, these properties hold such promise for revolutionary advances that Geim and Novoselov were awarded the 2010 Nobel Prize a mere six years after their achievement.
Regan and Mecklenburg are part of a UCLA effort to develop extremely fast transistors using this new material.
"We wanted to calculate the amplification of a graphene transistor," Mecklenburg said. "Our collaboration was building them and needed to know how well they were going to work."
This calculation involved understanding how light interacts with the electrons in graphene.
The electrons in graphene move by hopping from carbon atom to carbon atom, as if hopping on a chessboard. The graphene chessboard tiles are triangular, with the dark tiles pointing "up" and light ones pointing "down." When an electron in graphene absorbs a photon, it hops from light tiles to dark ones. Mecklenburg and Regan showed that this transition is equivalent to flipping a spin from "up" to "down."
In other words, confining the electrons in graphene to specific, discrete positions in space gives them spin. This spin, which derives from the special geometry of graphene's honeycomb lattice, is in addition to and distinct from the usual spin carried by the electron. In graphene the additional spin reflects the unresolved chessboard-like structure to the space that the electron occupies.
"My adviser [Regan] spent his Ph.D. studying the structure of the electron," Mecklenburg said. "So he was very excited to see that spin can emerge from a lattice. It makes you wonder if the usual electron spin could be generated in the same way."
"It's not yet clear if this work will be more useful in particle or condensed matter physics," Regan said, "but it would be odd if graphene's honeycomb structure was the only lattice capable of generating spin."
The California NanoSystems Institute at UCLA is an integrated research facility located at UCLA and UC Santa Barbara. Its mission is to foster interdisciplinary collaborations in nanoscience and nanotechnology; to train a new generation of scientists, educators and technology leaders; to generate partnerships with industry; and to contribute to the economic development and the social well-being of California, the United States and the world. The CNSI was established in 2000 with $100 million from the state of California. An additional $850 million of support has come from federal research grants and industry funding. CNSI members are drawn from UCLA's College of Letters and Science, the David Geffen School of Medicine, the School of Dentistry, the School of Public Health and the Henry Samueli School of Engineering and Applied Science. They are engaged in measuring, modifying and manipulating atoms and molecules — the building blocks of our world. Their work is carried out in an integrated laboratory environment. This dynamic research setting has enhanced understanding of phenomena at the nanoscale and promises to produce important discoveries in health, energy, the environment and information technology.
For more news, visit the UCLA Newsroom and follow us on Twitter.
Jennifer Marcus | EurekAlert!
Hope to discover sure signs of life on Mars? New research says look for the element vanadium
22.09.2017 | University of Kansas
22.09.2017 | Forschungszentrum MATHEON ECMath
Plants and algae use the enzyme Rubisco to fix carbon dioxide, removing it from the atmosphere and converting it into biomass. Algae have figured out a way to increase the efficiency of carbon fixation. They gather most of their Rubisco into a ball-shaped microcompartment called the pyrenoid, which they flood with a high local concentration of carbon dioxide. A team of scientists at Princeton University, the Carnegie Institution for Science, Stanford University and the Max Plank Institute of Biochemistry have unravelled the mysteries of how the pyrenoid is assembled. These insights can help to engineer crops that remove more carbon dioxide from the atmosphere while producing more food.
A warming planet
Our brains house extremely complex neuronal circuits, whose detailed structures are still largely unknown. This is especially true for the so-called cerebral cortex of mammals, where among other things vision, thoughts or spatial orientation are being computed. Here the rules by which nerve cells are connected to each other are only partly understood. A team of scientists around Moritz Helmstaedter at the Frankfiurt Max Planck Institute for Brain Research and Helene Schmidt (Humboldt University in Berlin) have now discovered a surprisingly precise nerve cell connectivity pattern in the part of the cerebral cortex that is responsible for orienting the individual animal or human in space.
The researchers report online in Nature (Schmidt et al., 2017. Axonal synapse sorting in medial entorhinal cortex, DOI: 10.1038/nature24005) that synapses in...
Whispering gallery mode (WGM) resonators are used to make tiny micro-lasers, sensors, switches, routers and other devices. These tiny structures rely on a...
Using ultrafast flashes of laser and x-ray radiation, scientists at the Max Planck Institute of Quantum Optics (Garching, Germany) took snapshots of the briefest electron motion inside a solid material to date. The electron motion lasted only 750 billionths of the billionth of a second before it fainted, setting a new record of human capability to capture ultrafast processes inside solids!
When x-rays shine onto solid materials or large molecules, an electron is pushed away from its original place near the nucleus of the atom, leaving a hole...
For the first time, physicists have successfully imaged spiral magnetic ordering in a multiferroic material. These materials are considered highly promising candidates for future data storage media. The researchers were able to prove their findings using unique quantum sensors that were developed at Basel University and that can analyze electromagnetic fields on the nanometer scale. The results – obtained by scientists from the University of Basel’s Department of Physics, the Swiss Nanoscience Institute, the University of Montpellier and several laboratories from University Paris-Saclay – were recently published in the journal Nature.
Multiferroics are materials that simultaneously react to electric and magnetic fields. These two properties are rarely found together, and their combined...
19.09.2017 | Event News
12.09.2017 | Event News
06.09.2017 | Event News
22.09.2017 | Life Sciences
22.09.2017 | Medical Engineering
22.09.2017 | Physics and Astronomy