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ScienceWeek
MATERIALS SCIENCE: ON COPPER OXIDE SUPERCONDUCTIVITY
The following points are made by Michael Norman (Nature 2004 427:692):
1) Throughout the history of superconductivity, optical spectroscopy -- through the scattering of light by a material --has been a vital tool. It was the existence of a gap in the excitation-energy spectrum of electrons, first observed in optical studies, that set Bardeen on the path to the celebrated Bardeen-Cooper-Schrieffer theory of superconductivity. That theory, in which electrons move as Cooper pairs, is now the established description of the low-temperature phenomenon.
2) For copper oxides, the transition temperature at which they become superconducting is much higher than in other materials --hence the name "high-temperature superconductors". Hwang et al(1) have looked at the so-called optical self-energy of a bismuth-containing copper oxide (known as Bi-2212). This self-energy quantifies the deviation of the measured energy spectrum of electrons in the material from that predicted by the simple Drude theory of elementary metals. In the Drude theory, electrons are treated as hard spheres that travel in straight lines between collisions; deviations from this behavior are thus a measure of the strength of the many-body interactions that the electrons undergo.
3) Hwang et al(1) found that for temperatures above the superconducting transition temperature this self-energy has a rather broad and featureless distribution up to very high electron excitation energies. Such behavior is inconsistent with that expected if the moving electrons are interacting with phonons -- vibrations in the atomic lattice -- as occurs in low-temperature superconductors. Instead, Hwang et al(1) conclude that the self-energy distribution is due to interactions between the electrons themselves. This finding supports a large body of theoretical work that argues that copper oxide superconductors are indeed fundamentally different from their low-temperature counterparts. As Hwang et al(1) also suggest, this optical self-energy can be considered as a measure of the "glue" that binds electrons into Cooper pairs, binding that in turn gives rise to superconductivity.(2-5)
References (abridged):
1. Hwang, J., Timusk, T. & Gu, G. D. Nature 427, 714-717 (2004).
2. Kaminski, A. et al. Phys. Rev. Lett. 86, 1070-1073 (2001)
3. Lanzara, A. et al. Nature 412, 510-514 (2001)
4. Johnson, P. D., et al. Phys. Rev. Lett. 87, 177007 (2001)
5. Rossat-Mignod, J. et al. Physica C 185-189, 86-92 (1991)
Nature http://www.nature.com/nature
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CONDENSED MATTER: SUPERCONDUCTIVITY AND COOPER PAIRS
The following points are made by Piers Coleman (Nature 2003 424:625):
1) One of the outstanding mysteries in condensed-matter physics is that the most perfect conductors so far discovered -- the high-temperature superconductors -- are more like insulators than metals. Superconductivity, the flow without resistance of current through some materials, usually only occurs at very low temperatures. Conventional superconductivity develops in metals, but high-temperature superconductivity (at about 90 K) occurs in insulating copper oxide ceramics when small amounts of charge are injected by chemical doping.
2) The quantum physicist Paul Dirac (1902-1984) once remarked that the equations needed to understand most of physics are known, but are far too complicated to solve. Lurking in this complexity lies the astounding ability of matter to develop new types of collective behavior, such as superconductivity and magnetism. The equation that accurately describes all of this behavior is the many-body Schroedinger equation. This involves two essential elements: the wavefunction, which is related to the probability of finding the electrons (or other particles) of a system in a given spatial configuration; and the Hamiltonian, a function that determines the energy of a system from its wavefunction. In a typical material, the number of particles tracked by the wavefunction is of the order of Avogadro's number -- 6 x 10^(23). This level of complexity means that understanding collective behavior, such as that of electrons in a superconductor, depends on the creative abstraction of both the Hamiltonian and the wavefunction into a much simpler model that captures the essence of the physics.
3) Conventionally, superconductivity develops in a conducting metal when the electrons bind together to form "Cooper pairs". Each electron spins like a tiny top, and in a Cooper pair the electron spins are aligned in an antiparallel configuration. Soon after high-temperature superconductivity was discovered, it was noted that the insulating state from which high-temperature superconductivity arises is a special kind of insulator, called a "Mott insulator". The mobile electrons in a high-temperature superconductor hop from one copper atom to the next, but repel one another because of their negative charges. When these repulsive forces are large enough, the electrons are prevented from ever doubly occupying a given copper atom.
4) In undoped copper oxide superconductors, there is precisely one mobile electron per copper atom, so the restriction on double occupancy causes the electrons to remain localized, at one electron per site. Strong magnetic forces between the localized electrons at different sites cause their spins to orient together in oppositely aligned pairs. According to the "resonating valence bond" (RVB) model of high-temperature superconductivity, these pairs form a fluid that resonates between the sites in a fashion reminiscent of the Cooper pairs inside a superconductor. When charge is introduced into this insulating background of pairs (through doping with impurity atoms), the RVB state evolves directly from insulator to superconductor.
Nature http://www.nature.com/nature
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MATERIALS SCIENCE: ON HIGH-TEMPERATURE SUPERCONDUCTORS
At temperatures close to absolute zero (-273.15 degrees Celsius), the thermal, electric, and magnetic properties of many substances undergo dramatic changes. One such phenomenon is superconductivity, which occurs below a critical temperature specific for each substance that exhibits the effect.
Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes (1853-1926), who was awarded the Nobel Prize for Physics in 1913 for his low temperature research. Kamerlingh Onnes found that the electrical resistance of a mercury wire suddenly disappears when the wire is cooled below a temperature of approximately 4 degrees kelvin. Similar behavior (but at widely varying critical temperatures) has been found in approximately 25 other chemical elements, including lead and tin, and in thousands of alloys and chemical compounds. Apart from these known superconducting materials, all other substances investigated to within fractions of a degree of absolute zero show normal (non-superconducting) resistance to the flow of electric currents.
For almost 50 years after the discovery of superconductivity by Kamerlingh Onnes, there was no successful fundamental theory that could explain the phenomenon. Finally, in 1957, an apparently satisfactory theory of superconductivity was presented by John Bardeen (1908-1991), Leon N. Cooper, and John R. Schrieffer, who all shared the Nobel Prize for Physics in 1972. The theory is now called the BCS theory of superconductivity.
The essential aspect of BCS theory is the grouping of electrons in superconductors in pairs ("Cooper pairs"), with the motions of all the Cooper pairs within a single superconductor correlated, i.e., the population of Cooper-pair electrons constituting a system that functions essentially as a single entity. (In quantum mechanical terms, each Cooper pair consists of electrons of opposite spins, thus forming a spin-zero single *boson, and the population of bosons form a *Bose-Einstein condensate described by a single wave function.) Application of an electric voltage to the superconductor causes all Cooper pairs to move, the movement constituting a current. When the voltage is removed, current continues to flow indefinitely because the Cooper pairs (as members of a coherent condensate) are not scattered by the atomic lattice. As a superconductor is warmed, its Cooper pairs separate into individual electrons, and the material becomes non-superconducting.
Such was the theory of superconductivity for nearly 30 years, the theory successfully predicting the behavior of superconducting materials with critical temperatures close to absolute zero. In 1986, Karl A. Mueller and J. Georg Bednorz discovered that certain materials exhibit superconductivity at temperatures as high as 35 degrees kelvin, and compounds retaining superconductivity at temperatures as high as 160 degrees kelvin have since been found. Mueller and Bednorz were awarded the Nobel Prize in Physics in 1987 for their work with high-temperature superconductors. Such high-temperature superconductors all contain copper and oxygen atoms that form planes or chains of atoms in the crystal, and it is believed that anisotropy is an important factor in their superconducting behavior. These materials are ceramic oxides, and because they are superconducting at temperatures easily obtainable with liquid nitrogen, great effort has been expended to find applications for these substances. But problems of brittleness, instabilities, and the aggregation of impurities at surfaces have slowed progress. Nevertheless, in contrast to superconducting ceramics, superconducting metals and their alloys must be cooled to near absolute zero with liquid helium, a process much more expensive than cooling with liquid nitrogen. Superconducting ceramics thus remain an important frontier of research in materials science.
In terms of theory, what is significant is that BCS theory apparently cannot provide a complete explanation of the behavior of high-temperature ceramic superconductors. A version of BCS theory may explain how superconductivity occurs in certain ceramic materials, but no complete theory of high-temperature superconductivity in ceramic materials has yet been proposed.
Recently, researchers in superconductivity were startled when J. Nagamatsu et al (5 authors at 2 installations, JP) (Nature 1 Mar 01 410:63) (in a paper consisting of only 3 short paragraphs) reported the discovery of bulk superconductivity in the simple and readily available compound magnesium diboride [MgB(sub2)], with magnetization and resistivity measurements establishing a transition temperature of 39 degrees kelvin, the highest known critical temperature for a non-copper-oxide (non-ceramic) bulk superconductor. [Editor's note: The surprise of condensed-matter physicists at this new discovery is reminiscent of the surprise of the same community at the discovery by Mueller and Bednorz in 1986 of high-temperature ceramic superconductors. See related background material below.]
The following points are made by Robert J. Cava (Nature 2001 410:23):
1) The author points out that in the ideal case of superconductivity, the zero-resistance state is absolute: electrons flowing in a continuous loop of superconducting wire below the critical temperature could theoretically flow for the age of the Universe and never lose any energy. But in the real world there are losses, e.g., from microscopic inhomogeneities, and the ideal is never obtained. Nevertheless, devices made with superconducting materials have resistances orders of magnitude lower than those of devices made with conventional conductors. This low resistance to current means that large currents (on the order of 10^(6) amperes per square centimeter of wire cross-section) can be passed without significant heating. For example, the magnets in magnetic resonance imaging instruments now in common use are made from metal-alloy superconducting wires, and these magnets are cooled below the critical temperature of the metal-alloy by immersion in liquid helium at 4.2 degrees kelvin.
2) The author points out there are two reasons for the current excitement concerning the discovery of superconductivity in magnesium diboride: a) Early indications are that magnesium diboride becomes superconducting by the BCS mechanism, so that unlike high-temperature copper-oxide superconductors, magnesium diboride appears to be a "conventional" superconductor. Magnesium diboride has the highest critical temperature known for a chemically stable, bulk compound of this type, and this suggests the possible existence of even higher superconducting critical temperatures in conventional and readily available materials yet to be investigated. b) The second reason for excitement is that it has proved so difficult to make useful wires of superconducting ceramics. This new report by J. Nagamatsu et al raises the possibility that superconducting materials based on magnesium diboride may eventually be able to carry more current than copper oxide superconductors. With a critical temperature of 39 degrees kelvin, there is also the possibility that magnesium diboride superconductors would not need to be cooled by liquid helium, but could be cooled by electrical refrigerators. The author concludes: "How much this discovery changes the path of materials physics depends on whether magnesium diboride is a solitary example of a new way of making high-temperature superconductors or whether it represents only the tip of an iceberg."
Nature http://www.nature.com/nature
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Notes by ScienceWeek:
boson: According to current physics, all particles in nature are either fermions or bosons, with fermions (always elementary particles) having half-integer spin (spin-states characterized by half-integer multiples of Planck's constant divided by 2pi), and bosons (all other particles) having integer spin (spin-states characterized by integer multiples of Planck's constant divided by 2pi). In general, bosons are particles that obey *Bose-Einstein statistics, and they include photons, *pi mesons, all nuclei having an even number of particles, and all particles with integer or zero spin.
Bose-Einstein statistics: Bose-Einstein statistics is the statistical mechanics of a system of indistinguishable particles for which there is no restriction on the number of particles that may simultaneously exist in the same quantum energy state. Particles that obey Bose-Einstein statistics are called "bosons".
Bose-Einstein condensate: In general, "Bose-Einstein condensation" is a phenomenon occurring in a macroscopic system consisting of a relatively large number of bosons at a sufficiently low temperature (microkelvins down to nanokelvins) in which a significant fraction of the particles occupy a single quantum state of lowest energy (the ground state). In an atomic Bose-Einstein condensate, several thousand atoms essentially become a single atom, a "superatom", and this effect has been observed experimentally with atoms of rubidium and lithium, the atoms trapped and cooled by special methods.
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