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  • richardmitnick 1:44 pm on April 27, 2018 Permalink | Reply
    Tags: , , Majorana fermion science, , , , , Topological insulators, Topological quantum computation,   

    From Physics Illinois: “Topological insulator �flips� for superconductivity” 

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    Physics Illinois

    U Illinois Physics bloc

    4/27/2018
    Siv Schwink

    Topology meets superconductivity through innovative reverse-order sample preparation.

    1
    (L-R) Professor of Physics James Eckstein, his graduate student Yang Bai, and Professor of Physics Tai-Chang Chiang pose in front of the atomic layer by layer molecular beam epitaxy system used to grow the topological insulator thin-film samples for this study, in the Eckstein laboratory at the University of Illinois. Photo by L. Brian Stauffer, University of Illinois at Urbana-Champaign.

    A groundbreaking sample preparation technique has enabled researchers at the University of Illinois at Urbana-Champaign and the University of Tokyo to perform the most controlled and sensitive study to date of a topological insulator (TI) closely coupled to a superconductor (SC). The scientists observed the superconducting proximity effect—induced superconductivity in the TI due to its proximity to the SC—and measured its relationship to temperature and the thickness of the TI.

    TIs with induced superconductivity are of paramount interest to physicists because they have the potential to host exotic physical phenomena, including the elusive Majorana fermion—an elementary particle theorized to be its own antiparticle—and to exhibit supersymmetry—a phenomenon reaching beyond the standard model that would shed light on many outstanding problems in physics. Superconducting TIs also hold tremendous promise for technological applications, including topological quantum computation and spintronics.

    Naturally occurring topological superconductors are rare, and those that have been investigated have exhibited extremely small superconducting gaps and very low transition temperatures, limiting their usefulness for uncovering the interesting physical properties and behaviors that have been theorized.

    TIs have been used in engineering superconducting topological superconductors (TI/SC), by growing TIs on a superconducting substrate. Since their experimental discovery in 2007, TIs have intrigued condensed matter physicists, and a flurry of theoretical and experimental research taking place around the globe has explored the quantum-mechanical properties of this extraordinary class of materials. These 2D and 3D materials are insulating in their bulk, but conduct electricity on their edges or outer surfaces via special surface electronic states which are topologically protected, meaning they can’t be easily destroyed by impurities or imperfections in the material.

    But engineering such TI/SC systems via growing TI thin films on superconducting substrates has also proven challenging, given several obstacles, including lattice structure mismatch, chemical reactions and structural defects at the interface, and other as-yet poorly understood factors.

    2
    The �flip-chip� cleavage-based sample preparation: (A) A photo and a schematic diagram of assembled Bi2Se3(0001)/Nb sample structure before cleavage. (B) Same sample structure after cleavage exposing a �fresh� surface of the Bi2Se3 film with a pre-determined thickness. Image courtesy of James Eckstein and Tai-Chang-Chiang, U. of I. Department of Physics and Frederick Seitz Materials Research Laboratory.

    Now, a novel sample-growing technique developed at the U. of I. has overcome these obstacles. Developed by physics professor James Eckstein in collaboration with physics professor Tai-Chang Chiang, the new “flip-chip” TI/SC sample-growing technique allowed the scientists to produce layered thin-films of the well-studied TI bismuth selenide on top of the prototypical SC niobium—despite their incompatible crystalline lattice structures and the highly reactive nature of niobium.

    These two materials taken together are ideal for probing fundamental aspects of the TI/SC physics, according to Chiang: “This is arguably the simplest example of a TI/SC in terms of the electronic and chemical structures. And the SC we used has the highest transition temperature among all elements in the periodic table, which makes the physics more accessible. This is really ideal; it provides a simpler, more accessible basis for exploring the basics of topological superconductivity,” Chiang comments.

    The method allows for very precise control over sample thickness, and the scientists looked at a range of 3 to 10 TI layers, with 5 atomic layers per TI layer. The team’s measurements showed that the proximity effect induces superconductivity into both the bulk states and the topological surface states of the TI films. Chiang stresses, what they saw gives new insights into superconducting pairing of the spin-polarized topological surface states.

    “The results of this research are unambiguous. We see the signal clearly,” Chiang sums up. “We investigated the superconducting gap as a function of TI film thickness and also as a function of temperature. The results are pretty simple: the gap disappears as you go above niobium’s transition temperature. That’s good—it’s simple. It shows the physics works. More interesting is the dependence on the thickness of the film. Not surprisingly, we see the superconducting gap reduces for increasing TI film thickness, but the reduction is surprisingly slow. This observation raises an intriguing question regarding how the pairing at the film surface is induced by coupling at the interface.”

    Chiang credits Eckstein with developing the ingenious sample preparation method. It involves assembling the sample in reverse order, on top of a sacrificial substrate of aluminum oxide, commonly known as the mineral sapphire. The scientists are able to control the specific number of layers of TI crystals grown, each of quintuple atomic thickness. Then a polycrystalline superconducting layer of niobium is sputter-deposited on top of the TI film. The sample is then flipped over and the sacrificial layer that had served as the substrate is dislodged by striking a “cleavage pin.” The layers are cleaved precisely at the interface of the TI and aluminum oxide.

    3
    A close-up shot of the atomic layer by layer molecular beam epitaxy system used to grow the topological insulator thin-film samples for this study, located in the Eckstein laboratory at the University of Illinois. Photo by L. Brian Stauffer, University of Illinois at Urbana-Champaign.

    Eckstein explains, “The ‘flip-chip’ technique works because the layers aren’t strongly bonded—they are like a stack of paper, where there is strength in the stack, but you can pull apart the layers easily. Here, we have a triangular lattice of atoms, which comes in packages of five—these layers are strongly bonded. The next five layers sit on top, but are weakly bonded to the first five. It turns out, the weakest link is right at the substrate-TI interface. When cleaved, this method gives a pure surface, with no contamination from air exposure.”

    The cleavage was performed in an ultrahigh vacuum, within a highly sensitive instrument at the Institute for Solid State Physics at the University of Tokyo capable of angle-resolved photoemission spectroscopy (ARPES) at a range of temperatures.

    Chiang acknowledges, “The superconducting features occur at very small energy scales—it requires a very high energy resolution and very low temperatures. This portion of the experiment was completed by our colleagues in the University of Tokyo, where they have the instruments with the sensitivity to get the resolution we need for this kind of study. We couldn’t have done this without this international collaboration.”

    “This new sample preparation method opens up many new avenues in research, in terms of exotic physics, and, in the long term, in terms of possible useful applications—potentially even including building a better superconductor. It will allow preparation of samples using a wide range of other TIs and SCs. It could also be useful in miniaturization of electronic devices, and in spintronic computing, which would require less energy in terms of heat dissipation,” Chiang concludes.

    Eckstein adds, “There is a lot of excitement about this. If we can make a superconducting TI, theoretical predictions tell us that we could find a new elementary excitation that would make an ideal topological quantum bit, or qubit. We’re not there yet, and there are still many things to worry about. But it would be a qubit whose quantum mechanical wave function would be less susceptible to local perturbations that might cause dephasing, messing up calculations.”

    These findings were published online on 27 April 2018 in the journal Science Advances.

    See the full article here .

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  • richardmitnick 1:05 pm on November 29, 2017 Permalink | Reply
    Tags: , Topological insulators,   

    From U Sidney via Science Alert: “Physicists Just Invented an Essential Component Needed For Quantum Computers” 

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    University of Sidney

    Science Alert

    29 NOV 2017
    MIKE MCRAE

    1
    (The University of Sydney)

    They’re using a new state of matter for this.

    In 2016, the Nobel Prize in Physics went to three British scientists for their work on superconductors and superfluids, which included the explanation of a rather odd phase of matter.

    Now, for the first time, their discovery has a practical application – shrinking an electrical component to a size that will help quantum computers reach a scale that just might make them useful.

    In a collaboration with Stanford University in the US, a team of scientists from the University of Sydney and Microsoft have used the newly found phase of matter – topological insulator – in shrinking an electrical component called a circulator 1,000 times smaller.

    That’s super good news when it comes to squeezing more qubits into a small enough space.

    If you missed the fuss last year, a trio of physicists received the Nobel Prize for discovering that under certain conditions some materials could easily conduct electrons along their surface, but remain an insulator within.

    Most importantly, they discovered cases where matter transitioned between states without breaking something called symmetry, as happens when water atoms rearrange into ice or vapour.

    As we shrink electrical components down to virtually atomic scales, the way electrons move in different dimensions becomes increasingly important.

    Enter the qubit – a chunky piece of electronics that uses the probabilities of an unmeasured bit of matter to perform calculations classical computers can’t hope to match.

    We can make qubits in a variety of ways, and are getting pretty good at stringing them together in ever larger numbers.

    But shrinking qubits to sizes small enough that we can shove hundreds of thousands into a small-enough space is a challenge.

    “Even if we had millions of qubits today, it is not clear that we have the classical technology to control them,” says David Reilly, a physicist at the University of Sydney and Director of Microsoft Station Q.

    “Realising a scaled-up quantum computer will require the invention of new devices and techniques at the quantum-classical interface.”

    One such device is called a circulator, which is kind-of like a roundabout for electrical signals, ensuring information heads in one direction only.

    Until now, the smallest versions of this hardware could be held in the palm of your hand.

    This is now set to change as scientists have shown a magnetised wafer made of a particular topological insulator could do the job, and be made 1,000 times smaller than existing components.

    “Such compact circulators could be implemented in a variety of quantum hardware platforms, irrespective of the particular quantum system used,” says the study’s lead author, Alice Mahoney.

    In many respects, we’re still at the pre-vacuum-tube and magnetic tape phase of quantum computers – they’re more promise than practical.

    But if we keep seeing advances like this, it won’t be long before we’ll be bringing you news of quantum computers cracking problems which leave our best supercomputers gasping.

    This research was published in Nature Communications.

    See the full article here .

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  • richardmitnick 5:31 pm on July 20, 2017 Permalink | Reply
    Tags: , , If all the states in a group of bands are filled with electrons then the electrons cannot move and the material is an insulator, , , , The approach combined tools from such disparate fields as chemistry and mathematics also physics and materials science, The nearly century-old band theory of solids considered one of the early landmark achievements of quantum mechanics, The research shows that symmetry and topology also chemistry and physics all have a fundamental role to play in our understanding of materials, The theory describes the electrons in crystals as residing in specific energy levels known as bands, Topological insulators   

    From Princeton: “Researchers find path to discovering new topological materials, holding promise for technological applications” 

    Princeton University
    Princeton University

    July 20, 2017
    No writer credit

    1
    Researchers have discovered how to identify new examples of topological materials, which have unique and desirable electronic properties. The technique involves finding the connection between band theory, which describes the energy levels of electrons in a solid, with a material’s topological nature. The disconnected bands indicate the material is a topological insulator. Image courtesy of Nature.

    Researchers find path to discovering new topological materials, holding promise for technological applications.

    An international team of researchers has found a way to determine whether a crystal is a topological insulator — and to predict crystal structures and chemical compositions in which new ones can arise. The results, published July 20 in the journal Nature, show that topological insulators are much more common in nature than currently believed.

    Topological materials, which hold promise for a wide range of technological applications due to their exotic electronic properties, have attracted a great deal of theoretical and experimental interest over the past decade, culminating in the 2016 Nobel Prize in physics. The materials’ electronic properties include the ability of current to flow without resistance and to respond in unconventional ways to electric and magnetic fields.

    Until now, however, the discovery of new topological materials occurred mainly by trial and error. The new approach described this week [see above reference to the Nature article] allows researchers to identify a large series of potential new topological insulators. The research represents a fundamental advance in the physics of topological materials and changes the way topological properties are understood.

    The team included: at Princeton University, Barry Bradlyn and Jennifer Cano, both associate research scholars at the Princeton Center for Theoretical Science, Zhijun Wang, a postdoctoral research associate, and B. Andrei Bernevig, professor of physics; professors Luis Elcoro and Mois Aroyo at the University of the Basque Country in Bilbao; assistant professor Maia Garcia Vergniory of University of the Basque Country and Donostia International Physics Center (DIPC) in Spain; and Claudia Felser, professor at the Max Planck Institute for Chemical Physics of Solids in Germany.

    “Our approach allows for a much easier way to find topological materials, avoiding the need for detailed calculations,” Felser said. “For some special lattices, we can say that, regardless of whether a material is an insulator or a metal, something topological will be going on,” Bradlyn added.

    Until now, of the roughly 200,000 materials catalogued in materials databases, only around a few hundred are known to host topological behavior, according to the researchers. “This raised the question for the team: Are topological materials really that scarce, or does this merely reflect an incomplete understanding of solids?” Cano said.

    To find out, the researchers turned to the nearly century-old band theory of solids, considered one of the early landmark achievements of quantum mechanics. Pioneered by Swiss-born physicist Felix Bloch and others, the theory describes the electrons in crystals as residing in specific energy levels known as bands. If all the states in a group of bands are filled with electrons, then the electrons cannot move and the material is an insulator. If some of the states are unoccupied, then electrons can move from atom to atom and the material is capable of conducting an electrical current.

    Because of the symmetry properties of crystals, however, the quantum states of electrons in solids have special properties. These states can be described as a set of interconnected bands characterized by their momentum, energy and shape. The connections between these bands, which on a graph resemble tangled spaghetti strands, give rise to topological behaviors such as those of electrons that can travel on surfaces or edges without resistance.

    The team used a systematic search to identify many previously undiscovered families of candidate topological materials. The approach combined tools from such disparate fields as chemistry, mathematics, physics and materials science.

    First, the team characterized all the possible electronic band structures arising from electronic orbitals at all the possible atomic positions for all possible crystal patterns, or symmetry groups, that exist in nature, with the exception of magnetic crystals. To search for topological bands, the team first found a way to enumerate all allowed non-topological bands, with the understanding that anything left out of the list must be topological. Using tools from group theory, the team organized into classes all the possible non-topological band structures that can arise in nature.

    Next, by employing a branch of mathematics known as graph theory — the same approach used by search engines to determine links between websites — the team determined the allowed connectivity patterns for all of the band structures. The bands can either separate or connect together. The mathematical tools determine all the possible band structures in nature — both topological and non-topological. But having already enumerated the non-topological ones, the team was able to show which band structures are topological.

    By looking at the symmetry and connectivity properties of different crystals, the team identified several crystal structures that, by virtue of their band connectivity, must host topological bands. The team has made all of the data about non-topological bands and band connectivity available to the public through the Bilbao Crystallographic Server. “Using these tools, along with our results, researchers from around the world can quickly determine if a material of interest can potentially be topological,” Elcoro said.

    The research shows that symmetry, topology, chemistry and physics all have a fundamental role to play in our understanding of materials, Bernevig said. “The new theory embeds two previously missing ingredients, band topology and orbital hybridization, into Bloch’s theory and provides a prescriptive path for the discovery and characterization of metals and insulators with topological properties.”

    David Vanderbilt, a professor of physics and astronomy at Rutgers University who was not involved in the study, called the work remarkable. “Most of us thought it would be many years before the topological possibilities could be catalogued exhaustively in this enormous space of crystal classes,” Vanderbilt said. “This is why the work of Bradlyn and co-workers comes as such a surprise. They have developed a remarkable set of principles and algorithms that allow them to construct this catalogue at a single stroke. Moreover, they have combined their theoretical approach with materials database search methods to make concrete predictions of a wealth of new topological insulator materials.”

    The theoretical underpinnings for these materials, called “topological” because they are described by properties that remain intact when an object is stretched, twisted or deformed, led to the awarding of the Nobel Prize in physics in 2016 to F. Duncan M. Haldane, Princeton’s Sherman Fairchild University Professor of Physics; J. Michael Kosterlitz of Brown University; and David J. Thouless of the University of Washington.

    Chemistry and physics take different approaches to describing crystalline materials, in which atoms occur in regularly ordered patterns or symmetries. Chemists tend to focus on the atoms and their surrounding clouds of electrons, known as orbitals. Physicists tend to focus on the electrons themselves, which can carry electric current when they hop from atom to atom and are described by their momentum.

    “This simple fact — that the physics of electrons is usually described in terms of momentum, while the chemistry of electrons is usually described in terms of electronic orbitals — has left material discovery in this field at the mercy of chance,” Wang said.

    “We initially set out to better understand the chemistry of topological materials — to understand why some materials have to be topological,” Vergniory said.

    Aroyo added, “What came out was, however, much more interesting: a way to marry chemistry, physics and mathematics that adds the last missing ingredient in a century-old theory of electronics, and in the present-day search for topological materials.”

    Funding for the study was provided by the U.S. Department of Energy (DE-SC0016239), the U.S. National Science Foundation (EAGER DMR-1643312 and MRSEC DMR-1420541), and the U.S. Office of Naval Research (N00014-14-1-0330). Additional funding came from a Simons Investigator Award, the David & Lucile Packard Foundation, and Princeton University’s Eric and Wendy Schmidt Transformative Technology Fund. Funding was also provided by the Spanish Ministry of Economy and Competitiveness (FIS2016-75862-P and FIS2013-48286-C2-1-P), the Government of the Basque Country (project IT779-13), and the Spanish Ministry of Economy and Competitiveness and European Federation for Regional Development (MAT2015-66441-P).

    The study, Topological quantum chemistry, by Barry Bradlyn, Luis Elcoro, Jennifer Cano, Maia Garcia Vergniory, Zhijun Wang, Claudia Felser, Mois Aroyo and B. Andrei Bernevig, was published in the journal Nature on July 20, 2017.

    See the full article here .

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  • richardmitnick 12:55 pm on June 26, 2017 Permalink | Reply
    Tags: 1T’-WTe2, , , , , , , , , Topological insulators   

    From LBNL: “2-D Material’s Traits Could Send Electronics R&D Spinning in New Directions” 

    Berkeley Logo

    Berkeley Lab

    June 26, 2017
    Glenn Roberts Jr
    geroberts@lbl.gov
    (510) 486-5582

    1
    This animated rendering shows the atomic structure of a 2-D material known as 1T’-WTe2 that was created and studied at Berkeley Lab’s Advanced Light Source. (Credit: Berkeley Lab.)

    An international team of researchers, working at the Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) and UC Berkeley, fabricated an atomically thin material and measured its exotic and durable properties that make it a promising candidate for a budding branch of electronics known as “spintronics.”

    The material – known as 1T’-WTe2 – bridges two flourishing fields of research: that of so-called 2-D materials, which include monolayer materials such as graphene that behave in different ways than their thicker forms; and topological materials, in which electrons can zip around in predictable ways with next to no resistance and regardless of defects that would ordinarily impede their movement.

    At the edges of this material, the spin of electrons – a particle property that functions a bit like a compass needle pointing either north or south – and their momentum are closely tied and predictable.

    2
    A scanning tunneling microscopy image of a 2-D material created and studied at Berkeley Lab’s Advanced Light Source (orange, background). In the upper right corner, the blue dots represent the layout of tungsten atoms and the red dots represent tellurium atoms. (Credit: Berkeley Lab.)

    This latest experimental evidence could elevate the material’s use as a test subject for next-gen applications, such as a new breed of electronic devices that manipulate its spin property to carry and store data more efficiently than present-day devices. These traits are fundamental to spintronics.

    The material is called a topological insulator because its interior surface does not conduct electricity, and its electrical conductivity (the flow of electrons) is restricted to its edges.

    “This material should be very useful for spintronics studies,” said Sung-Kwan Mo, a physicist and staff scientist at Berkeley Lab’s Advanced Light Source (ALS) who co-led the study, published today in Nature Physics.

    LBNL/ALS

    “We’re excited about the fact that we have found another family of materials where we can both explore the physics of 2-D topological insulators and do experiments that may lead to future applications,” said Zhi-Xun Shen, a professor in Physical Sciences at Stanford University and the Advisor for Science and Technology at SLAC National Accelerator Laboratory who also co-led the research effort.

    “This general class of materials is known to be robust and to hold up well under various experimental conditions, and these qualities should allow the field to develop faster,” he added.

    The material was fabricated and studied at the ALS, an X-ray research facility known as a synchrotron. Shujie Tang, a visiting postdoctoral researcher at Berkeley Lab and Stanford University, and a co-lead author in the study, was instrumental in growing 3-atom-thick crystalline samples of the material in a highly purified, vacuum-sealed compartment at the ALS, using a process known as molecular beam epitaxy.

    The high-purity samples were then studied at the ALS using a technique known as ARPES (or angle-resolved photoemission spectroscopy), which provides a powerful probe of materials’ electron properties.

    3
    Beamline 10.0.1 at Berkeley Lab’s Advanced Light Source enables researchers to both create and study atomically thin materials. (Credit: Roy Kaltschmidt/Berkeley Lab.)

    “After we refined the growth recipe, we measured it with ARPES. We immediately recognized the characteristic electronic structure of a 2-D topological insulator,” Tang said, based on theory and predictions. “We were the first ones to perform this type of measurement on this material.”

    But because the conducting part of this material, at its outermost edge, measured only a few nanometers thin – thousands of times thinner than the X-ray beam’s focus – it was difficult to positively identify all of the material’s electronic properties.

    So collaborators at UC Berkeley performed additional measurements at the atomic scale using a technique known as STM, or scanning tunneling microscopy. “STM measured its edge state directly, so that was a really key contribution,” Tang said.

    The research effort, which began in 2015, involved more than two dozen researchers in a variety of disciplines. The research team also benefited from computational work at Berkeley Lab’s National Energy Research Scientific Computing Center (NERSC).

    NERSC Cray Cori II supercomputer

    LBL NERSC Cray XC30 Edison supercomputer

    Two-dimensional materials have unique electronic properties that are considered key to adapting them for spintronics applications, and there is a very active worldwide R&D effort focused on tailoring these materials for specific uses by selectively stacking different types.

    “Researchers are trying to sandwich them on top of each other to tweak the material as they wish – like Lego blocks,” Mo said. “Now that we have experimental proof of this material’s properties, we want to stack it up with other materials to see how these properties change.”

    A typical problem in creating such designer materials from atomically thin layers is that materials typically have nanoscale defects that can be difficult to eliminate and that can affect their performance. But because 1T’-WTe2 is a topological insulator, its electronic properties are by nature resilient.

    “At the nanoscale it may not be a perfect crystal,” Mo said, “but the beauty of topological materials is that even when you have less than perfect crystals, the edge states survive. The imperfections don’t break the key properties.”

    Going forward, researchers aim to develop larger samples of the material and to discover how to selectively tune and accentuate specific properties. Besides its topological properties, its “sister materials,” which have similar properties and were also studied by the research team, are known to be light-sensitive and have useful properties for solar cells and for optoelectronics, which control light for use in electronic devices.

    The ALS and NERSC are DOE Office of Science User Facilities. Researchers from Stanford University, the Chinese Academy of Sciences, Shanghai Tech University, POSTECH in Korea, and Pusan National University in Korea also participated in this study. This work was supported by the Department of Energy’s Office of Science, the National Science Foundation, the National Science Foundation of China, the National Research Foundation (NRF) of Korea, and the Basic Science Research Program in Korea.

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  • richardmitnick 12:19 pm on December 12, 2016 Permalink | Reply
    Tags: , , , , , Topological insulators   

    From Hopkins and Rutgers: “Between two worlds: Exotic insulator may hold clue to key mystery of modern physics” 

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    Johns Hopkins University

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    Rutgers University

    Dec 6, 2016
    Arthur Hirsch

    Scientists experiment with material that straddles world of classical physics and hidden quantum realm

    Experiments using laser light and pieces of gray material the size of fingernail clippings may offer clues to a fundamental scientific riddle: what is the relationship between the everyday world of classical physics and the hidden quantum realm that obeys entirely different rules?

    1
    N. Peter Armitage

    “We found a particular material that is straddling these two regimes,” said N. Peter Armitage, an associate professor of physics at Johns Hopkins University who led the research for the paper just published in the journal Science. Six scientists from Johns Hopkins and Rutgers University were involved in the work on materials called topological insulators, which can conduct electricity on their atoms-thin surface, but not in their insides.

    Topological insulators were predicted in the 1980s, first observed in 2007, and have been studied intensively since. Made from any number of hundreds of elements, these materials have the capacity to show quantum properties that usually appear only at the microscopic level, but here appear in a material visible to the naked eye.

    The experiments reported in Science establish these materials as a distinct state of matter “that exhibits macroscopic quantum mechanical effects,” Armitage said. “Usually we think of quantum mechanics as a theory of small things, but in this system quantum mechanics is appearing on macroscopic length scales. The experiments are made possible by unique instrumentation developed in my laboratory.”

    In the experiments reported in Science, the elements bismuth and selenium make up dark gray material samples—each a few millimeters long and of different thicknesses—that were hit with “THz” light beams that are invisible to the unaided eye. Researchers measured the reflected light as it moved through the material samples and found indicators of a quantum state of matter.

    Specifically, they found that as the light was transmitted through the material, the wave rotated a specific amount, which is related to physical constants that are usually only measurable in atomic scale experiments. The amount matched predictions of what would be possible in this quantum state.

    The results add to scientists’ understanding of topological insulators, but also may contribute to the larger subject that Armitage says is the central question of modern physics: what is the relationship between the macroscopic classical world, and the microscopic quantum world from which it arises?

    Scientists since the early 20th century have struggled with the question of how one set of physical laws governing objects above a certain size can co-exist alongside a different set of laws governing the atomic and subatomic scale. How does classical mechanics emerge from quantum mechanics, and where is the threshold that divides the realms?

    Those questions remain to be answered, but topological insulators could be part of the solution.

    “It’s a piece of the puzzle,” said Armitage, who worked on the experiments along with Liang Wu, who was a graduate student at Johns Hopkins when the work was done; Maryam Salehi of the Rutgers University Department of Material Science and Engineering; and Nikesh Koirala, Jisoo Moon, and Sean Oh of the Rutgers University Department of Physics and Astronomy.

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