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  • richardmitnick 8:48 am on March 20, 2017 Permalink | Reply
    Tags: Anderson limit, Cooper Pairs, How small can superconductors be?, , P.W. Anderson, Parity effect, , , Richardson-Gaudin models   

    From phys.org: “How small can superconductors be?” 


    March 20, 2017
    Lisa Zyga

    Topographic image of a lead nanocrystal used in the study. Scale bar: 10 nm. Credit: Vlaic et al. Nature Communications

    For the first time, physicists have experimentally validated a 1959 conjecture that places limits on how small superconductors can be. Understanding superconductivity (or the lack thereof) on the nanoscale is expected to be important for designing future quantum computers, among other applications.

    In 1959, physicist P.W. Anderson conjectured that superconductivity can exist only in objects that are large enough to meet certain criteria. Namely, the object’s superconducting gap energy must be larger than its electronic energy level spacing—and this spacing increases as size decreases. The cutoff point (where the two values are equal) corresponds to a volume of about 100 nm3. Until now it has not been possible to experimentally test the Anderson limit due to the challenges in observing superconducting effects at this scale.

    In the new study published in Nature Communications, Sergio Vlaic and coauthors at the University Paris Sciences et Lettres and French National Centre for Scientific Research (CNRS) designed a nanosystem that allowed them to experimentally investigate the Anderson limit for the first time.

    The Anderson limit arises because, at very small scales, the mechanisms underlying superconductivity essentially stop working. In general, superconductivity occurs when electrons bind together to form Cooper pairs. Cooper pairs have a slightly lower energy than individual electrons, and this difference in energy is the superconducting gap energy. The Cooper pairs’ lower energy inhibits electron collisions that normally create resistance. If the superconducting gap energy gets too small and vanishes—which can occur, for example, when the temperature increases—then the electron collisions resume and the object stops being a superconductor.

    The Anderson limit shows that small size is another way that an object may stop being a superconductor. However, unlike the effects of increasing the temperature, this is not because smaller objects have a smaller superconducting gap energy. Instead, it arises because smaller crystals have fewer electrons, and therefore fewer electron energy levels, than larger crystals do. Since the total possible electron energy of an element stays the same, regardless of size, smaller crystals have larger spacings between their electron energy levels than larger crystals do.

    According to Anderson, this large electronic energy level spacing should pose a problem, and he expected superconductivity to disappear when the spacing becomes larger than the superconducting gap energy. The reason for this, generally speaking, is that one consequence of increased spacing is a decrease in potential energy, which interferes with the competition between kinetic and potential energy that is necessary for superconductivity to occur.

    To investigate what happens to the superconductivity of objects around the Anderson limit, the scientists in the new study prepared large quantities of isolated lead nanocrystals ranging in volume from 20 to 800 nm3.

    Although they could not directly measure the superconductivity of such tiny objects, the researchers could measure something called the parity effect, which results from superconductivity. When an electron is added to a superconductor, the additional energy is partly affected by whether there is an even or odd number of electrons (the parity), which is due to the electrons forming Cooper pairs. If the electrons don’t form Cooper pairs, there is no parity effect, indicating no superconductivity.

    Although the parity effect has previously been observed in large superconductors, this study is the first time that it has been observed in small nanocrystals approaching the Anderson limit. In accordance with Anderson’s predictions from more than 50 years ago, the researchers observed the parity effect for larger nanocrystals, but not for the smallest nanocrystals below approximately 100 nm3.

    The results not only validate the Anderson conjecture, but also extend to a more general area, the Richardson-Gaudin models. These models are equivalent to the conventional theory of superconductivity, the Bardeen Cooper Schrieffer theory, for very small objects.

    “Our experimental demonstration of the Anderson conjecture is also a demonstration of the validity of the Richardson-Gaudin models,” coauthor Hervé Aubin at the University Paris Sciences et Lettres and CNRS told Phys.org. “The Richardson-Gaudin models are an important piece of theoretical works because they can be solved exactly and apply to a wide range of systems; not only to superconducting nanocrystals but also to atomic nuclei and cold fermionic atomic gas, where protons and neutrons, which are fermions like electrons, can also form Cooper pairs.”

    On the more practical side, the researchers expect the results to have applications in future quantum computers.

    “One of the most interesting applications of superconducting islands is their use as Cooper pair boxes employed in quantum bits, the elemental unit of a hypothetical quantum computer,” Aubin said. “So far, Cooper pair boxes used in qubits are much larger than the Anderson limit. Upon reducing the size of the Cooper pair box, quantum computer engineers will eventually have to cope with superconductivity at the Anderson limit.”

    See the full article here .

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  • richardmitnick 10:19 am on October 17, 2016 Permalink | Reply
    Tags: , Cooper Pairs, , , ,   

    From John A Paulson School of Engineering and Applied Sciences: “A new spin on superconductivity” 

    Harvard School of Engineering and Applied Sciences
    John A Paulson School of Engineering and Applied Sciences

    October 14, 2016
    Leah Burrows


    Researchers from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have made a discovery that could lay the foundation for quantum superconducting devices. Their breakthrough solves one the main challenges to quantum computing: how to transmit spin information through superconducting materials.

    Every electronic device — from a supercomputer to a dishwasher — works by controlling the flow of charged electrons. But electrons can carry so much more information than just charge; electrons also spin, like a gyroscope on axis.

    Harnessing electron spin is really exciting for quantum information processing because not only can an electron spin up or down — one or zero — but it can also spin any direction between the two poles. Because it follows the rules of quantum mechanics, an electron can occupy all of those positions at once. Imagine the power of a computer that could calculate all of those positions simultaneously.

    A whole field of applied physics, called spintronics, focuses on how to harness and measure electron spin and build spin equivalents of electronic gates and circuits.

    By using superconducting materials through which electrons can move without any loss of energy, physicists hope to build quantum devices that would require significantly less power.

    But there’s a problem.

    According to a fundamental property of superconductivity, superconductors can’t transmit spin. Any electron pairs that pass through a superconductor will have the combined spin of zero.

    In work published recently in Nature Physics, the Harvard researchers found a way to transmit spin information through superconducting materials.

    “We now have a way to control the spin of the transmitted electrons in simple superconducting devices,” said Amir Yacoby, Professor of Physics and of Applied Physics at SEAS and senior author of the paper.

    It’s easy to think of superconductors as particle super highways but a better analogy would be a super carpool lane as only paired electrons can move through a superconductor without resistance.

    These pairs are called Cooper Pairs and they interact in a very particular way. If the way they move in relation to each other (physicists call this momentum) is symmetric, then the pair’s spin has to be asymmetric — for example, one negative and one positive for a combined spin of zero. When they travel through a conventional superconductor, Cooper Pairs’ momentum has to be zero and their orbit perfectly symmetrical.

    But if you can change the momentum to asymmetric — leaning toward one direction — then the spin can be symmetric. To do that, you need the help of some exotic (aka weird) physics.

    Superconducting materials can imbue non-superconducting materials with their conductive powers simply by being in close proximity. Using this principle, the researchers built a superconducting sandwich, with superconductors on the outside and mercury telluride in the middle. The atoms in mercury telluride are so heavy and the electrons move so quickly, that the rules of relativity start to apply.

    “Because the atoms are so heavy, you have electrons that occupy high-speed orbits,” said Hechen Ren, coauthor of the study and graduate student at SEAS. “When an electron is moving this fast, its electric field turns into a magnetic field which then couples with the spin of the electron. This magnetic field acts on the spin and gives one spin a higher energy than another.”

    So, when the Cooper Pairs hit this material, their spin begins to rotate.

    “The Cooper Pairs jump into the mercury telluride and they see this strong spin orbit effect and start to couple differently,” said Ren. “The homogenous breed of zero momentum and zero combined spin is still there but now there is also a breed of pairs that gains momentum, breaking the symmetry of the orbit. The most important part of that is that the spin is now free to be something other than zero.”

    The team could measure the spin at various points as the electron waves moved through the material. By using an external magnet, the researchers could tune the total spin of the pairs.

    “This discovery opens up new possibilities for storing quantum information. Using the underlying physics behind this discovery provides also new possibilities for exploring the underlying nature of superconductivity in novel quantum materials,” said Yacoby.

    This research was coauthored by Sean Hart, Michael Kosowsky, Gilad Ben-Shach, Philipp Leubner, Christoph Brüne, Hartmut Buhmann, Laurens W. Molenkamp and Bertrand I. Halperin.

    See the full article here .

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    Through research and scholarship, the Harvard School of Engineering and Applied Sciences (SEAS) will create collaborative bridges across Harvard and educate the next generation of global leaders. By harnessing the power of engineering and applied sciences we will address the greatest challenges facing our society.

    Specifically, that means that SEAS will provide to all Harvard College students an introduction to and familiarity with engineering and technology as this is essential knowledge in the 21st century.

    Moreover, our concentrators will be immersed in the liberal arts environment and be able to understand the societal context for their problem solving, capable of working seamlessly withothers, including those in the arts, the sciences, and the professional schools. They will focus on the fundamental engineering and applied science disciplines for the 21st century; as we will not teach legacy 20th century engineering disciplines.

    Instead, our curriculum will be rigorous but inviting to students, and be infused with active learning, interdisciplinary research, entrepreneurship and engineering design experiences. For our concentrators and graduate students, we will educate “T-shaped” individuals – with depth in one discipline but capable of working seamlessly with others, including arts, humanities, natural science and social science.

    To address current and future societal challenges, knowledge from fundamental science, art, and the humanities must all be linked through the application of engineering principles with the professions of law, medicine, public policy, design and business practice.

    In other words, solving important issues requires a multidisciplinary approach.

    With the combined strengths of SEAS, the Faculty of Arts and Sciences, and the professional schools, Harvard is ideally positioned to both broadly educate the next generation of leaders who understand the complexities of technology and society and to use its intellectual resources and innovative thinking to meet the challenges of the 21st century.

    Ultimately, we will provide to our graduates a rigorous quantitative liberal arts education that is an excellent launching point for any career and profession.

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