One of the lessons of quantum physics is that any set of subatomic particles bound together by mutual attractions have quite distinct states of relative motion determined by how the particles interact, and that changing the particles’ motion from one such state to another requires that their energy and momentum change by appropriate discrete finite amounts. Electrons bound within a metal to the lattice[Wikipedia] of its positive ions[Wikipedia] are no exception. Under ordinary conditions in our usual environment, an electric field applied to the metal can accelerate its electrons so they absorb energy from the field and flow among the ions. The ion lattice, which vibrates randomly with greater agitation the higher the metal’s temperature, affects what states of motion the electrons can have. While an electric field acting on unbound electrons in empty space would accelerate them indefinitely, the electrons in a metal sometimes collide with the randomly vibrating lattice and lose energy that they’ve gained from the field.
If a collision can’t transfer just the right amount of momentum and energy to the ions, the electron’s motion won’t change to one of the different possible states and the electron will just continue on its way, much as it would in empty space. But if the collision transfers the right amount of energy to the ion lattice, the lattice’s motion gets more agitated (i.e., the lattice gets warmer), and the electron’s motion will change to a different state that starts out slower before accelerating in response to the electric field again. If the energy and momentum differences between possible motions are small enough for collisions to make the changes possible, the ion lattice will resist the electrons’ motion so that they bump along through the metal around some constant average speed. The lower the metal’s temperature, the less agitated the ion lattice’s motion, and the less it resists the flow of electrons by absorbing enough of their energy to knock them into one of the initially-slower states of motion.
Even before the quantum mechanics of electron-ion interactions was known, the decrease of metals’ electrical resistance with temperature had been observed, and its disappearance at absolute zero temperature was already suspected. So it was a surprise when Heike Kammerlingh Onnes[Wikipedia] found in 1911 that the resistance of mercury suddenly gets ahead of its downward trend, abruptly vanishing at a critical temperature above absolute zero. The same sudden loss of resistance somewhere above zero kelvins was later found for many metals and alloys. Kammerlingh Onnes initially called this phenomenon “supraconductivity”, but later adopted the name “superconductivity” by which it’s known today.
Superconductivity, as an interesting phenomenon that also has a number of technological uses, was studied by many people over the next few decades to figure out why it happens. The clues found in those years of experiments included the discovery that metals below the critical temperature also expel magnetic fields from their interiors—something that a simple loss of electrical resistance wouldn’t cause by itself. Another important clue was the mid-20th-century finding that a material’s critical temperature depends in a particular way on the masses of its ions.
For many materials, the sudden change in electric and magnetic behavior turned out to be explainable as the effect of a new kind of electron motion becoming possible at lower temperatures, as the theory formulated by John Bardeen[Wikipedia], Leon Cooper[Wikipedia], and John Schrieffer[Wikipedia] first showed in the 1950s.[Wikipedia] While the like negative charges of any material’s electrons repel each other, they also attract the lattice’s positively-charged ions towards them, distorting the shape of the lattice as the electrons move through it. Bardeen, Cooper, and Schrieffer showed that, when certain materials cool below their critical temperature, their ion lattices can distort enough for the electrons’ attraction to it to overcome their own mutual repulsion. This makes it possible for the electrons to flow together as a unit whose energy and momentum are so different from any state of independent electron motion that lattice collisions cannot transfer enough momentum or energy to remove any electrons from the collective motion. The material thus becomes superconductive, its electron flow proceeding without resistance.
The mathematical details of the Bardeen-Cooper-Schrieffer theory (BCS theory) not only fit the known facts about the superconductors already known when the theory was worked out, but about many others discovered since, including some nonmetallic ones: each known superconductor’s behavior was consistent with electrons that could move as an undisturbed unit when their mutual repulsion was overcome by attraction to the superconductor’s atomic lattice. However, numerous superconductors discovered later, beginning with a ceramic in 1986 whose own critical temperature was 12 kelvins[Wikipedia] higher than the highest critical temperature known before, don’t seem to become superconducting through the same mechanism, and differ in other ways that may or may not relate to that fact. Some of these superconductors, having much higher critical temperatures that range above 100 kelvins, can operate with much less (and much cheaper) refrigeration; for that reason and others they offer new technological capabilities.
A complete understanding of how high-temperature superconductors work, still lacking at present, might help people discover new ones more systematically and less accidentally, and even design them. Clues to this understanding may come from high-temperature superconductors of course, but also from other superconductors whose mechanisms, while similar, don’t superconduct at high temperatures themselves. Efforts to produce, use, and understand high-temperature superconductors are ongoing, as can be seen from a sample of research reports available through OSTI’s SciTech Connect.
A set of slides for lectures on superconductivity[SciTech Connect] at the University of Salerno by Los Alamos National Laboratory researcher Boris Maiorov, after illustrating some superconductor basics, focuses on superconductors’ magnetic properties and how they affect the materials’ ability to conduct current. As mentioned above, when a superconducting material in a magnetic field is cooled enough to become superconducting, it will expel at least some of the field from its interior—and if the material is like one of the earliest-known superconductors, it’ll expel practically all of the magnetic field. At the material’s surface, the field will be at full strength, but will exponentially decrease with depth below the surface, becoming practically zero within a short, characteristic field-penetration depth for that material. Later on, examples of a second type of superconductor were discovered, which similarly expel all magnetic field below a certain critical strength, but will only expel some of it if the field is between that strength and a higher critical strength. The field not confined to the superconductor’s surface is confined to individual tubes running through its bulk, each tube having a magnetic flux equal to Planck’s constant h[Wikipedia] divided by the charge on one pair of electrons 2e,[Wikipedia] or just over 2 femtowebers.[Wikipedia, Wikipedia] Around the length of each magnetic-flux tube, supercurrents of electrons circulate as a vortex without resistance. This second, type-II behavior characterizes some low-temperature superconductors, and all the high-temperature ones.
When a supercurrent flows through a type-II superconductor that contains supercurrent vortices, the vortices interact with supercurrent flowing through the material and affect the amount of energy required to disrupt it. The main supercurrent tends to move the vortices around, and easily does so if the material’s ion lattice has a uniform structure and composition throughout. But where the lattice structure is missing some atoms, has extra atoms, or is made of different kinds of atoms from those in the surrounding lattice, the vortices can be pinned in place, and the main supercurrent can be larger without being disrupted.
Like many discoveries with obvious potential, high-temperature superconductors present technical challenges to that potential’s realization. Maiorov’s slide set mentions two kinds of challenges. One kind of challenge relates to how supercurrents that run through a material interact with magnetic-flux vortices in it; the other relates to how the ceramics of which many high-temperature superconductors are made can be formed into wires. Other specific challenges are addressed in two recent patents and a brief final report on an industrial/national lab cooperative project.
The patent “Method for producing microstructured templates and their use in providing pinning enhancements in superconducting films deposited thereon”[DOepatents], by inventors at Oak Ridge National Laboratory, describes an efficient method for producing a high-temperature superconducting tape whose ion lattice contains the kind of defects that can pin superconducting vortices to specific places, thereby allowing the tape to carry higher-density supercurrents than it might otherwise when exposed to external magnetic fields, which “are prevalent in most commercial and industrial applications” as the patent notes.
While the first known high-temperature superconductor, lanthanum barium copper oxide (LBCO), set a new critical-temperature record (35 kelvins) when it was discovered, it still required expensive refrigeration with liquid hydrogen or liquid helium to make it superconduct. A different copper oxide, yttrium barium copper oxide (YBCO), was the first superconductor that would work above 77 kelvins, a temperature achievable with much cheaper liquid nitrogen, so this type of superconductor has been widely investigated. A recent investigation involving YBCO is described in “Development of YBCO Superconductor for Electric Systems: Cooperative Research and Development Final Report, CRADA Number CRD-04-150”.[SciTech Connect] This report describes success in addressing superconductors’ susceptibility to suddenly becoming resistive due to local defects, overload, or failures in power supply or cooling systems. A superconductor that becomes resistive while carrying current will heat up rapidly and may produce arcing and undergo large mechanical forces as the current suddenly decreases and its magnetic field collapses.[Wikipedia] The report’s authors, working under a Cooperative Research And Development Agreement between the National Renewable Energy Laboratory and SuperPower, Inc., successfully electrodeposited silver and copper layers on yttrium barium copper oxide (YBCO) superconductors, which can bypass electric current around the YBCO if it fails or its critical current is exceeded. The report lists Energy Department funding for the research as well as three published papers and a patent application that resulted.
The search for new high-temperature superconductors did not end with the discovery of copper oxides. A more-recently discovered type, iron pnictide [Wikipedia], is the focus of another new patent (“Low resistivity contact to iron-pnictide superconductors”[DOepatents]) from inventors at Ames Laboratory. As the patent states, “feeding electrical current into a superconductor generates heat dissipation in the contacts and degrades maximum attainable current value”, which low-resistance electrical contacts can minimize. “However,” as the patent notes, “the selection of contact materials heavily depends on the surface reactivity of the materials in contact”, which requires much experimenting to determine. An illustrative embodiment of the invention uses tin or a tin-based material between a metallic conductor and an iron-pnictide superconductor to connect the metal and iron-pnictide together with a surface resistivity on the order of one nano-ohm[Wikipedia, Wikipedia] per square centimeter.
Superconductors’ electromagnetic properties don’t end with their ability to superconduct electric currents and expel static magnetic fields. Light, which consists of electromagnetic waves, can interact in interesting ways with superconductors. Terahertz light[Wikipedia] in particular can interact strongly with metamaterials[Wikipedia, Science Showcase] whose basic structural units are roughly one terahertz-wavelength in size.[Science Showcase] Metamaterials made with YBCO components are the subject of investigations by a collaboration of scientists at Los Alamos National Laboratory and Massachusetts Institute of Technology. Los Alamos researcher Nathaniel K. Grady presented data from this work at a SPIE Optics+Photonics conference last year on the response of YBCO metamaterials to terahertz light (“Response of High-Tc Superconductor Metamaterials to High Intensity THz Radiation”[SciTech Connect]). Metamaterials generally can be used to manipulate light in ways that ordinary materials can’t; superconducting metamaterials offer possibilities that may go beyond those offered by other metamaterials.
As mentioned above, research on high-temperature superconductors aims not only to overcome technical obstacles to their use but to understand how they work as well. Just as the study of specific low-temperature metallic superconductors showed patterns that suggested how all of them lose their electrical resistance under certain conditions, observing the behavior of different families of high-temperature superconductors and individual materials within those families should offer clues to the apparently different mechanism(s) behind their superconductivity. Several reports from Los Alamos National Laboratory and Stanford University’s SLAC National Accelerator Laboratory describe findings of this sort.
Supercurrents are stable because removing an electron from the supercurrent would require more energy than the electron can get from the ion lattice’s thermal motion; the greater the energy gap, the more stable the supercurrent. In ceramic high-temperature superconductors, there can even be different energy gaps corresponding to different supercurrents, because the ceramics superconduct along different planes of atoms within them instead of throughout their bulk as low-temperature metallic superconductors do. This fact comes up in the SLAC report “Enhanced Superconducting Gaps in Trilayer High-Temperature Bi2Sr2Ca2Cu3O10+d Cuprate Superconductor”[SciTech Connect] by researchers at the University of Tokyo, Hiroshima University, the high-energy physics laboratory KEK, and Stanford University. The ceramic family Bi2Sr2Ca2Cu3O10+d, whose individual members are distinguished by different values of d, has triple layers of copper oxide separated by calcium layers and surrounded by strontium-oxide layers, which in turn are surrounded by bismuth-oxide layers. The investigators exposed the ceramic to ultraviolet light which caused it to emit electrons, whose energies and directions of emission were measured[Wikipedia] to determine the gaps between the energies of superconducting and normally-conducting electrons in the inner and outer copper-oxide layers. The investigators find the outer layers’ energy gap between superconducting and normally-conducting electrons to be a sizeable 43 milli-electronvolts[Wikipedia, Wikipedia] and the inner layers’ gap an even larger 60 milli-electronvolts, and hypothesize reasons for the large values.
The same experimental technique (known as angle-resolved photoemission spectroscopy), one commonly used to study solid materials’ electron distributions, was used by other researchers from Stanford, SLAC, Rice University, the University of Houston, Nanjing University, and Lawrence Berkeley National Laboratory to study some newly-discovered iron-based superconductors. Unlike other iron-based superconductors, the ones described in the report act as insulators rather than normally-conducting metals when they’re not in their superconducting state. The report, “Observation of Temperature-Induced Crossover to an Orbital-Selective Mott Phase in AxFe2-ySe2 (A=K, Rb) Superconductors”[SciTech Connect], provides evidence that when these materials are warmed above their critical temperatures, electrons in certain states that moved freely beforehand among the materials’ ions become confined, each to a small volume, because other electrons’ repulsion inhibits their motion. This type of electron confinement, known as Mott insulation,[Wikipedia] differs from that of other electrical insulators in which electrons are confined because their attraction to the nearest positive ions is sufficiently strong.
Transitions between superconducting and insulating phases, or between superconducting and normally-conducting phases, are much like the more familiar transitions seen when many materials transform among solid, liquid, and gaseous phases. A material in a single phase has a uniform set of properties throughout; when it changes phase, it takes on a different uniform set of properties.[Wikipedia] Phase changes can follow changes in temperature, but they can also be brought on by changes in pressure or other parameters. Indeed, transition temperatures like melting points and boiling points can be affected by the ambient pressure (think of how water boils at less than 100 °C at high altitudes), which also means transition pressures can be affected by ambient temperature (e.g., water will boil at room temperature if you lower the air pressure to a few percent of standard atmospheric pressure).[Wikipedia] Similarly, the critical temperatures of superconductors decrease as their ambient magnetic fields increase (and their critical magnetic fields decrease as their temperatures increase). Both the ambient temperature and magnetic field also affect the materials’ critical superconducting currents—the largest currents they can superconduct. Another relevant variable, in an abstract sense, is the material’s composition. Although materials with different proportions and arrangements of elements are actually different materials, one can think of a spectrum of materials with slightly different proportions of the same atoms as a single material under slightly different conditions. One can thus consider a “single superconductor’s” critical temperature as dependent on its composition—for example, the critical temperature of YBa2Cu3O6+d varies with the number d.
The copper-oxide superconductors YBa2Cu3O6+d (yttrium barium copper oxide, or YBCO) and Bi2Sr2CaCu2O8+d (bismuth strontium calcium copper oxide) both exhibit some interesting phase changes as their temperature and composition are varied. Besides having a superconducting state, each material also exhibits something called a “pseudogap state” at temperatures between the critical temperature for superconductivity and another higher temperature which, like the critical temperature itself, depends on the oxide’s proportion of oxygen atoms. Reports on experiments to explore how these materials’ pseudogap and superconducting conditions are related[SciTech Connect; SciTech Connect] suggest that the conditions under which each material superconducts may actually correspond to more than one distinct phase, and involve phase changes quite different in nature from the transitions among solid, liquid, and gaseous phases.
In the pseudogap state, the distribution of possible electron motions over different electron energies resembles that of superconducting-state electron motions, but the pseudogap state exists at temperatures above the critical temperature for superconductivity. The pseudogap state also has a maximum temperature which, like the superconducting critical temperature, depends in copper-oxide superconductors on the proportion of oxygen to the material’s other elements. Researchers from Los Alamos, SLAC, and the University of British Columbia looked for evidence of thermodynamic differences between the pseudogap state and other states in yttrium barium copper oxide by exposing YBa2Cu3O6+d samples to ultrasound and measuring their mechanical resonances (“Ultrasonic signatures at the superconducting and the pseudogap phase boundaries in YBCO cuprates”[SciTech Connect]). For a YBa2Cu3O6.60 sample (YBa2Cu3O6+d with d=0.60), they found a sizeable change in the material’s stress/strain[Wikipedia] ratio, a thermodynamic parameter, above and below the highest temperature expected for the sample’s pseudogap state, based on a trend in these temperatures’ dependence on d observed from other measurements of different parameters.
Interestingly, these researchers’ further measurements of YBa2Cu3O6.98 (YBa2Cu3O6+d with d=0.98) showed a similar large change in stress/strain ratio at the temperature expected from the same trend, even though that temperature was below the critical temperature for superconductivity at that value of d. In other words, for d=0.98, YBa2Cu3O6+d exhibits two distinct phases that are both superconducting. The way the observed phase changes depend on the material’s temperature and composition suggests that the phases may be distinct for different values of d at absolute zero temperature, each phase representing profoundly different kinds of quantum-mechanical effects on the motion of electrons in the material. The exact value of d at absolute zero that would separate such different phases is known as a quantum critical point.[Wikipedia] While the data suggest a single critical point for YBCO, superconducting Bi2Sr2CaCu2O8+d appears to have two quantum critical points, each at a different value of d, as reported in “Phase Competition in Trisected Superconducting Dome”.[SciTech Connect] The investigators, at SLAC, Stanford, Lawrence Berkeley National Laboratory, Shandong University, Suranaree University of Technology, Tokyo Institute of Technology, the University of Tokyo, and Cornell University, made a comprehensive study of Bi2Sr2CaCu2O8+d at different temperatures and d using the angle-resolved photoemission spectroscopy technique.
Los Alamos researcher Eric D. Bauer’s slides “Discovery of Pu-based superconductors and relation to other classes of unconventional superconductors”[SciTech Connect] described findings of his collaborators at Los Alamos, the Institute for Transuranium Elements, and the Japan Atomic Energy Agency for a presentation at a conference last year on materials and mechanisms of superconductivity.[Reference] The slides compare the atomic arrangements of copper-oxide, iron-pnictide, and cerium-based superconductors with those of plutonium-based superconductors having formula PumMnX3m+2n (M being a metal and X representing gallium or indium), and illustrate known properties of several plutonium-based superconductors. The presentation discusses what these properties imply about how the materials’ electrons interact to make them superconduct, and notes evidence that one material of the PumMnX3m+2n family, PuRhIn5, has a quantum critical point.
“The scholar can hope to extract a new simplification from the complexity of facts only after he has become aware of complexities far greater than those he originally realized existed.”—Ithiel de Sola Pool,[Wikipedia] Symbols of Democracy, p. 73.
The earlier state of knowledge about how low-temperature superconductors work, before Bardeen, Cooper, and Schrieffer’s theory made sense of the clues already found, somewhat resembles our present understanding of high-temperature superconductors. There are at least two widely-favored competing hypotheses, but none of them clearly fit all the facts.[Wikipedia] Furthermore, discoveries like the evidence for high-temperature superconductors having quantum critical points suggests that a complete theory might have to take very recent discoveries into account, and that we may not even have all the relevant clues yet. In the end, though, we may find that a clear understanding of high-temperature superconductors, like the BCS theory of low-temperature superconductors, may turn out not to seem as complex as the array of natural processes it explains—a phenomenon seen repeatedly in science, at least from the time Isaac Newton showed how a few simple laws of motion and gravity could explain a huge, diverse array of processes in the natural world.
Prepared by Dr. William N. Watson, Physicist
DoE Office of Scientific and Technical Information