THEORY



Normal Metals

Metals conduct electricity via delocalized electrons within the metal lattice - in a metal, the atoms lose valence electrons to form a lattice of positively-charged cations. The valence electrons are then delocalized throughout the lattice, and are free to move between the cations - these electrons are the current carriers. When current flows in an ordinary conductor, for example copper wire, some energy is lost. In a light bulb or electric heater, the electrical resistance creates light and heat. In metals such as copper and aluminum, electricity is conducted as outer energy level electrons migrate as individuals from one atom to another. These atoms form a vibrating lattice within the metal conductor; the warmer the metal the more it vibrates. As the electrons begin moving through the maze, they collide with tiny impurities or imperfections in the lattice.When the electrons bump into these obstacles they fly off in all directions and lose energy in the form of heat.

Superconductors

Inside a superconductor the behavior of electrons is vastly different. The impurities and lattice are still there, but the movement of the superconducting electrons through the obstacle course is quite different. As the superconducting electrons travel through the conductor they pass unobstructed through the complex lattice. Because they bump into nothing and create no friction they can transmit electricity with no appreciable loss in the current and no loss of energy.


BCS Theory


The understanding of superconductivity was advanced in 1957 by three American physicists-John Bardeen, Leon Cooper, and John Schrieffer, through their Theories of Superconductivity, know as the BCS Theory. The BCS theory explains superconductivity at temperatures close to absolute zero. Cooper realized that atomic lattice vibrations were directly responsible for unifying the entire current. They forced the electrons to pair up into teams that could pass all of the obstacles which caused resistance in the conductor. These teams of electrons are known as Cooper pairs.
Cooper and his colleagues knew that electrons which normally repel one another must feel an overwhelming attraction in superconductors. The answer to this problem was found to be in phonons, packets of sound waves present in the lattice as it vibrates. Although this lattice vibration cannot be heard, its role as a moderator is indispensable.

According to the theory, as one negatively charged electron passes by positively charged ions in the lattice of the superconductor, the lattice distorts. This in turn causes phonons to be emitted which form a trough of positive charges around the electron. Before the electron passes by and before the lattice springs back to its normal position, a second electron is drawn into the trough. It is through this process that two electrons, which should repel one another, link up. The forces exerted by the phonons overcome the electrons' natural repulsion. The electron pairs are coherent with one another as they pass through the conductor in unison. The electrons are screened by the phonons and are separated by some distance. When one of the electrons that make up a Cooper pair and passes close to an ion in the crystal lattice, the attraction between the negative electron and the positive ion cause a vibration to pass from ion to ion until the other electron of the pair absorbs the vibration. The net effect is that the electron has emitted a phonon and the other electron has absorbed the phonon. It is this exchange that keeps the Cooper pairs together. However, the pairs are constantly breaking and reforming. Because electrons are indistinguishable particles, it is easier to think of them as permanently paired.

The BCS theory successfully shows that electrons can be attracted to one another through interactions with the crystalline lattice. This occurs despite the fact that electrons have the same charge. When the atoms of the lattice oscillate as positive and negative regions, the electron pair is alternatively pulled together and pushed apart without a collision. The electron pairing is favorable because it has the effect of putting the material into a lower energy state. When electrons are linked together in pairs, they move through the superconductor in an orderly fashion.

However, at higher temperatures and with different superconductor systems, the BCS theory has subsequently become inadequate to fully explain how superconductivity is occurring.

As long as the superconductor is cooled to very low temperatures, the Cooper pairs stay intact, due to the reduced molecular motion. As the superconductor gains heat energy the vibrations in the lattice become more violent and break the pairs. As they break, superconductivity diminishes. Superconducting metals and alloys have characteristic transition temperatures from normal conductors to superconductors called Critical Temperature (Tc). Below the superconducting transition temperature, the resistivity of a material is exactly zero. Superconductors made from different materials have different Tc values. Among ceramic superconductors, YBa2Cu3O7 TC, is about 90 K while for HBa2Ca2Cu308 it is up to 133 K.

However, there is a certain maximum current that these materials can be made to carry, above which they stop being superconductors. If too much current is pushed through a superconductor, it will revert to the normal state even though it may be below its transition temperature. The value of Critical Current Density (Jc) is a function of temperature; i.e., the colder you keep the superconductor the more current it can carry. For practical applications Jc values in excess of 1000 amperes per square millimeter (A/mm2) are preferred.

When a superconductor is cooled below its transition temperature (Tc) and a magnetic field is increased around it, the magnetic field remains around the superconductor. If the magnetic field is increased to a given point the superconductor will go to the normal resistive state.

The maximum value for the magnetic field at a given temperature is known as the critical magnetic field and is given the symbol Hc. Type II superconductors have two critical field strengths; Hc1, above which the field penetrates into the superconductor, and Hc2, above which superconductivity is destroyed. For all superconductors there exist a region of temperatures and magnetic fields within which the material is superconducting. Outside this region the material is normal. When the temperature is lowered to below the critical temperature, (Tc), the superconductor will "push" the field out of itself. It does this by creating surface currents in itself which produces a magnetic field exactly countering the external field, producing a "magnetic mirror". The superconductor becomes perfectly diamagnetic, canceling all magnetic flux in its interior. It is referred to as the Meissner Effect.


Types of superconductors


Type 1 superconductors - characterized as the "soft" superconductors - were discovered first and require the coldest temperatures to become superconductive. They exhibit a very sharp transition to a superconducting state and "perfect" diamagnetism. When an external magnetic field is applied to a Type I superconductor the induced magnetic field exactly cancels that applied field until there is an abrupt change from the superconducting state to the normal state. Type I superconductors are very pure metals that typically have critical fields (Hc) too low to be very useful.


Type II superconductors have much larger Hc values. The field strength at the surface of a neodymium-iron-boron magnet is approximately 16 kilogauss. The strongest type-I superconductor, pure lead has a critical field of about 800 gauss. YBCO superconductors have upper critical field values as high as 100tesla. Except for the elements vanadium, technetium and niobium, the Type 2 category of superconductors is comprised of metallic compounds and alloys. The recently-discovered superconducting "perovskites" (metal-oxide ceramics that normally have a ratio of 2 metal atoms to every 3 oxygen atoms) belong to this Type 2 group.

Many elements can be coaxed into a superconductive state with the application of high pressure. For example, phosphorus appears to be the Type 1 element with the highest Tc. But, it requires compression pressures of 2.5 Mbar to reach a Tc of 14-22 K.

Normally bulk carbon (amorphous, diamond, graphite, white) will not superconduct at any temperature. However, a Tc of 15K has been reported for elemental carbon when the atoms are configured as highly-aligned, single-walled nanotubes. Nanotubes made from other materials, like silicon, boron-nitride or tungsten-disulfide, may also exhibit superconductivity. Nanotubes are characterized as "Type 2" superconductors.

When fullerenes are doped with one or more alkali metals the fullerene becomes a "fulleride" and has produced Tc's ranging from 8 K for Na2Rb0.5Cs0.5C60 up to 40 K for Cs3C60. In 1993 researchers at the State University of New York at Buffalo reported Tc's between 60 K and 70 K for C-60 doped with the interhalogen compound ICl.

The highest Tc attained at ambient pressure has been 138 K by (Hg0.8Tl0.2)Ba2Ca2Cu3O8.33 In 1994, the record for Tc was 164K, under 30GPa of pressure, for HgBa2Ca2Cu3O8+x


The superconducting state is defined by three very important factors:

Each of these parameters is very dependant on the other two properties present. Maintaining the superconducting state requires that both the magnetic field and the current density, as well as the temperature, remain below the critical values, all of which depend on the material.

The highest values for Hc and Jc occur at 0 K, while the highest value for Tc occurs when H and J are zero. When electrons form Cooper pairs, they can share the same quantum wave-function or energy state. This results in a lower energy state for the superconductor. Tc and Hc are values where it becomes favorable for the electron pairs to break apart. For most practical applications, superconductors must be able to carry high currents and withstand high magnetic field without reverting to its normal state.


Quantum Mechanical or Microscopic Properties.



An example of microscopic properties is the phenomenon of electron tunneling in superconductors. Tunneling is a process arising from the wave nature of the electron. It occurs because of the transport of electrons through spaces that are forbidden by classical physics because of a potential barrier. The tunneling of a pair of electrons between superconductors separated by an insulating barrier was first discovered by Brian Josephson in 1962. Josephson discovered that if two superconducting metals were separated by a thin insulating barrier such as an oxide layer 10 to 20 angstroms thick, it is possible for electron pairs to pass through the barrier without resistance. This is known as the dc Josephson Effect, and is contrary to what happens in ordinary materials, where a potential difference must exist for a current to flow. The current that flows in through a D.C. Josephson junction has a critical current density which is characteristic of junction material and geometry.

A Josephson junction consists of two superconductors separated by a thin insulating barrier. Pairs of superconducting electrons will tunnel through the barrier. As long as the current is below the critical current for the junction, there will be zero resistance and no voltage drop across the junction.


Hysteresis (loop)



Hysteresis, as it applies to a superconductor, relates to the dynamic response of a superconductor to a strong magnetic field impinged upon it. As the strength of a nearby magnetic field (H) increases, the critical transition temperature (Tc) of a superconductor will decrease. And, at some point superconductivity will completely disappear, as it becomes "quenched". However, as the magnetic field is gradually withdrawn, the superconductor may NOT immediately return to a superconductive state. Herein lies the hysteresis. The graph of H-vs.-Tc is different retreating than it is advancing (creating a "loop" shape). This fact must be weighed carefully in high-current applications where the superconductor Hc may, even briefly, be exceeded; as significant power losses can result.


Deviation from Superconductivity



When combined with an element that has unusual magnetic properties - like holmium - "re-entrant" behavior can be in evidence in some borocarbides. Below Tc, where it should remain superconductive, there is a discordant temperature at which the material retreats to a "normal", non-superconductive state. And, not only the borocarbides recede from a superconductive state at extreme low temperatures. In the compounds HoMo6S8 (Chevrel) and ErRh4B4 superconductivity suddenly disappears at around 1K.

Ruthenium-cuprate is both a superconductor and a magnet. Unlike "normal" superconductors, this compound becomes diamagnetic at about one-half Tc.

There are many phase transitions that matter goes through on its way to another state (e.g. ice changing to water requires a sudden increase in heat energy). Among the superconductors this is also the case at Tc, Hc and Jc. However, a superconductor has been discovered that exhibits no measurable change in its specific heat (the amount of energy required to increase its temperature by one degree) while going through up to 3 different "critical" magnetic fields.