Stephen A. Fuqua (saf)

a Bahá'í, software engineer, and nature lover in Austin, Texas, USA

To Infinity and Beyond! The Physics of Superconductivity

Stephen A. Fuqua
September, 2002

Whilst its real-world applications are yet difficult to find, superconductivity may well prove to be one of the greatest discoveries of the 20th century. Herein we examine the physics behind this phenomenon, touch upon some of the applications we have developed thus far, and give some indication of the future development. Intended for the literate yet not necessarily technical audience, with no pictures or equations but plenty of links. Originally published at Kuro5hin, a techno-geek community website.

The phenomenon of superconductivity is a fascinating one that, like many other important discoveries in the 20th century, was not expected when first detected (c.f. penicillin, electron diffraction). At the time of its discovery in 1911, it was known that the conductivity of a metal–the ease with which electrical current passes through the substance–increases as it cools down. However, as Dutch physicist Heike Kamerlingh Onnes was investigating this property of metals, he stumbled across a never-before seen state of perfect conductivity in mercury when he cooled it with liquid helium (to 4.2 kelvin, or -268.80 C). Thus his experiments were the first to show that certain elements can have perfect–infinite!–conductivity at the right temperature, implying a loss of all resistance to electron flow (resistivity).

Electrical conductivity is what makes our microwave popcorn, and the television set we eat it in front of, possible: strands of metallic wire (generally copper) carry electric current from the power plant to our homes. The better the conductivity in the wire, the better it will be able to carry current to your home and supply the electricity needed to run your appliances. Certain physical properties of metals make them good conductors, while non-metals are generally considered insulators (that is, they will not pass a current through them, similar to your garden-variety Thermos).

But let us get a better understanding of conduction before we move on. Metals (conductors) allow small charged particles called electrons to flow through them, much like a tube through which water flows. Naturally, current–be it electrons or water–can flow back-wards or forwards through its conduit. The direction of flow is simply a matter of where you start it from.

Resistivity is the opposite of conductivity. Resistivity, as its name implies, is a literal blocking of flow–like a boulder in a stream or sandpaper that resists movement across a wooden block. And when you finally do get that sandpaper to move across the block, it requires a greater output of energy (or power, which is energy per unit of time) from you than just moving a regular piece of paper. Resistivity operates the same way: the more resistance a metal has, the more power is lost. This means that one must continually add energy–or, in the case of power lines, electricity–to the system in order to have a “constant” current flow. Without adding more energy, all of the electricity would eventually become lost power, adding unwanted dollars to your electric bill.

The resistance itself arises from intramolecular collisions. As the electrons flow through the metal, they often run into atoms. These atoms are then like the rocks in the creek that obstruct flow: resistance. Resistivity! Electrons, furthermore, belong to a class of particles (fermions) whose general behavior encourages collisions.

Fermions are not alone in the world of particles; there also exists a class of elementary particles called bosons. Primarily, two factors differentiate the two types: spin and group behavior. Spin is a quantum mechanical term for an intrinsic property of particles’, it can be in whole units (-1,-0,1,2, and so on) or in halves (-1/2,1/2,3/2, etc.). Bosons are those particles that have whole member spins, while fermions are all of those (including electrons) with half member spins. Aside from the spin, these two classes exhibit opposite behavior while in groups: while bosons like to act together, no two fermions can be in the same state at the same time (the Pauli Exclusion Principle). This is a quantum mechanical rule, a law of nature if you will. For fermions, this means that two electrons (or any other fermion particle) cannot both be doing the same thing in the same place at the same time. For instance, I once heard a joke that illustrates the matter well:

“Two electrons walk into a bar. The first asks for a gin and tonic. The second slams his hand on the table and says “Damn, that’s what I wanted!”

Because they cannot travel together, in the same state, there is much chaos in an electron’s life. And, as we all know, chaos leads to trouble. In this case, the chaos of energetic electrons traveling in such a haphazard way leads to many collisions, much like cattle stampeding every which way and bumping into each other.

Bosons are not like this, however. For bosons actually prefer to be in groups together, if a particle can prefer anything. Indeed, it turns out that the more bosons there are traveling together, the more likely it becomes that all of the bosons in a system will be in the same state. Thus it is not long before all of the bosons are traveling together under the same conditions.

When you cool down a material, you are doing the same thing as telling a child to “cool down.” That is, you are telling the child to have less energy and be less agitated. When you cool down the material, the electrons have less energy and are less agitated. With less energy, fewer collisions occur and the resistivity is lowered. Life becomes more ordered. Experience, however, had always shown that the resistivity would bottom out at a certain positive value different for each material. This bottoming out factor is due to the impurities in the substance, which will always cause some small amount of disorder.

Onnes’s discovery showed once again that experience fails to reveal the full story of reality. As he cooled the mercury down, he found that it exhibited the same tendency to decrease in resistivity as all other metals had. However, in 1908 Onnes had developed a system to liquefy helium (for which he won the Nobel Prize), which is much colder than the liquid nitrogen that was typically used in these kinds of experiments. Utilizing his new invention, he cooled the mercury down to 4.2 kelvin and noticed that all resistivity disappeared at this critical temperature. (The critical temperature is usually denoted Tc). He dubbed the new attribute superconductivity.

Though most good conductors (such as copper and silver) do not have superconductor characteristics, many other elements and even complex materials achieve zero resistance at critical temperatures. When Onnes performed his experiments, and indeed for many years to follow, there was no understanding of the mechanisms whereby superconductivity occurs. In 1957 John Bardeen (inventor of the transistor), Leon Cooper, and J. Robert Schrieffer formulated a theory to explain superconductivity, leading to their own Nobel.

BCS theory, as it is called for its inventors, postulates that electrons can actually form pairs which act as bosons instead of fermions (Cooper pairs). Though electrons normally repel each other due to their like charges, at very low temperatures the lattice structure of the atoms in a superconductor material becomes distorted by the passing of an electron. From this distortion arises a weak force that actually attracts a second electron to the first. Though the two are not physically bound together, it is as if they were in a three-legged race and forced to act cooperatively. Thus the two spin one half’s become one spin one and the Cooper pair acts like a boson instead of two separate fermions.

As bosons, the Cooper pairs naturally draw each other into cooperative states. At Tc, the pairs move together in the same direction and all with the same status: we have organization and no resistance. Instead of having a chaotic stampede, the cattle are now herded in an orderly manner. But as soon as you introduce even small amounts of energy, the cattle get agitated and start to move around. Pretty soon they are all scared and the order is completely destroyed. Back to resistivity we go.

Thus superconductors achieve zero resistivity when they reach Tc. And zero resistivity of course means that we now have perfect conductivity — zero power loss and a persistent current. In fact, some superconductors have been tested which are so good at conducting current that a current could last in them without power loss for 100,000 years.

Not only do these materials have perfect conductivity, but they also have an additional defining factor, the Meissner effect. The Meissner effect refers to the ability of superconductors to keep magnetic fields from passing through them. Instead the magnetic field flows around the superconductor. In a normal material, the magnetic field passes through the interior uniformly. In the superconductors state however, the Meissner effect kicks in and the flow of magnetic field around the material causes the material to repel permanent magnets. Combined, these two properties create a wealth of potential applications such as trains that levitate on superconductors magnets, efficient switches, amplifiers and other circuit components, power lines, and motors and other propulsion systems.

Unfortunately, the practical use of liquid helium is prohibitively expensive. Thankfully J. Georg Benorz and K. Alex Müller made a remarkable discovery in 1986: lanthanum-barium-copper-oxide (La2-xBaxCu4) achieves superconductivity at a critical temperature of 30 kelvin. Not only was this the highest Tc ever found, but the discovery also led to research in a whole new class of materials: ceramics. Later that same year, the ceramic YBa2Cu3O7 was discovered to exhibit zero resistance at 92 kelvin. For the first time, superconductivity was attainable at liquid nitrogen temperatures. Continuing research has brought that temperature up to 130 kelvin, still quite cold by human standards (-143° C), but easily attainable with off-the-shelf components. Strangely, BCS theory does not seem a good fit for high Tc superconductivity, and a new theory yet to be settled upon.

High temperature superconductivity gives new life to all of the applications that physicists once dreamed of, but never thought fiscally possible. While there is much work and research still to come, superconductors are beginning to show up in applied technologies, such as the Yamanashi Maglev Test Line (rail) in Japan, electric power transmission lines in Detroit, and enhanced Magnetic Resonance Imaging for medical testing. The cutting edge of experimental research is finding superconductivity in fullerenes, ferromagnets, and other materials, while the theoretical focuses on finding that new theory and determining an upper limit for any TC. The limits to superconductivity and its applications… well, they just may not exist. And thus it may be on the back of infinite conductivity that we ride to our Jetsonian future.