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1.1 Superconductivity

After successfully liquefying helium at 4.2 K in 1908, H. K. Onnes began to measure the resistivity of metals at these low temperatures.  Using high purity distilled mercury, Onnes found in 1911¹ that near 4.3 K the electrical resistivity in this metal began to vanish.  He later coined the term “supra-conductivity” which has since been modified to “superconductivity”.  The initial discovery of superconductivity in Hg was followed by the discovery of the same phenomenon in other elements such as lead (Pb).  Resistivity vs. temperature curve for a lead sample is provided in Figure 1.1.

Superconductivity seemed to be a unique phenomenon that had little influence on other physical properties until 1931 when W. H. Keesom and J. A. Kok observed an abrupt change in the specific heat of tin as it was cooled below its transition temperature.  This observation opened the door for investigations into other thermodynamic properties associated with the superconducting state.

Figure 1.1:     Resistivity vs. temperature of a thin film of the conventional superconductor, Pb (lead).

The first landmark discovery related to thermodynamics of super conductors was made in 1933 by Walther Meissner and Robert Ochsenfeld.²  The two scientists demonstrated the expulsion of magnetic field from within a superconducting metal as it is cooled below its transition temperature.  As the material is cooled below its transition, the superconductor creates an opposing magnetic field by generating a current.  It is thermodynamically favorable for a superconducting material to have electrons in a superconducting state below its transition temperature.  The generation of current to oppose a magnetic field requires energy, therefore it costs more energy when it must oppose a larger magnetic field.  If the energy required to expel the magnetic field exceeds the energy gained by entering the superconducting state, then superconductivity is lost.  This is why there is a magnetic field dependence on the superconducting state of a given material.  If a superconductor can exclude the magnetic field of a substance that has the gravitational force pushing down the mass of the magnet, the magnetic substance will levitate above the superconductor as seen in Illustrations 1.1 and 1.2.

In 1957,³ a theory that explains much of the fundamentals behind superconductivity was proposed.  Likewise, John Bardeen, Leon Cooper, and Robert Schrieffer devised a microscopic theory of superconductivity, which has since been described as the “BCS” theory.  This theory accurately predicts the superconducting properties of most metals and alloys.  Although it fails to predict the behavior of high-temperature superconductors, many scientists believe that a modified BCS theory may one day explain these new materials.  At the heart of BCS theory is that the pairs of electrons are “coupled” to the lattice vibrations, or phonons, within the superconductor.  These electrons are then able to move through the latticewithout resistance.

Illustration 1.1: Schematic demonstrating Meissner Effect where a) is the magnet without the presence of a superconductor and b) is with a superconductor excluding the magnetic field.

Illustration 1.2:     Photo of a rare-earth magnet levitating above a high-temperature superconductor pellet composed of  YBa₂Cu₃O_7-x that was chilled to 77K with liquid nitrogen.

Using the BCS theory, it was predicted that the upper temperature limit for superconductivity would be ~30 K.  Prior to the recent discovery of high-temperature superconducting materials, many scientists viewed skeptically the possibility of ever breaking this barrier.  By 1985, the highest transition temperature was found to be ~23 K for Nb₃N.  That record was shattered in 1986 by Karl Alex Müeller and Johannes Georg Bednorz⁴ at IBM, Zurich with the report of “Possible High T_c Superconductivity in the Ba-La-Cu-O System..”  Their paper reported an onset transition temperature of ~35 K.  The optimized composition was found later to be La_1.85Ba_0.15CuO₄.  Although the paper initially received little attention, as soon as the results were independently reproduced by other workers there was a worldwide search for new high-temperature superconductors, most based upon copper-oxide perovskite structures.  Bednorz and Müeller received the Noble prize in physics for their discovery in 1988.

After increasing the transition temperature of La_1.85Ba_0.15CuO₄ to as much as 52 K with the application of pressure,⁵ Paul Chu and colleagues began to investigate chemical substitutions that could internally mimic applied pressure.  In 1987, their research paid off with the discovery⁶ of YBa₂Cu₃O_7-x, a superconductor with a transition temperature of 93 K.  This important superconductor’s structure is shown in Illustration 1.3(a).  This discovery was particularly important because it identified the first superconductor which could be chilled into its superconducting state with liquid nitrogen.  Prior systems

Illustration 1.3:     Crystal structures of a) YBa₂Cu₃O_7-x and b) HgBa₂Ca₂Cu₃O₈.

Illustration 1.4:     Crystal structures of a) Bi₂Sr₂Ca₁Cu₂O₈ and b) Tl₂Ba₂Ca₂Cu₃O₁₀.

required liquid helium as their cryogen. Liquid nitrogen is about 1/20 the cost of liquid helium and requires less stringent insulation for storage.  This led many to foresee practical applications using this material.

By 1988, there were numerous reports of high-temperature superconducting phases.  Among these was the discovery of the Bi phase cuprates⁷ which were found to have transition temperatures of 80 K and 110 K.  The former material exhibits a composition of Bi₂Sr₂CaCu₂O₈ and the latter, Bi₂Sr₂Ca₂Cu₂O₁₀.  The Bi₂Sr₂CaCu₂O₈ structure is shown in Illustration 1.4(a).  Almost immediately following the report of the high transition temperature in the Bi phase cuprates, Tl₂Ba₂Ca₂Cu₃O₁₀,⁸ shown in Illustration 1.4(b), was discovered which is superconducting at 125 K.  This material held the record for highest transition temperature for several years until 1993 when superconductivity was discovered in the Hg-based cuprate systems,⁹ having a composition of roughly HgBa₂Ca₂Cu₃O₈.  One member of this class is seen in Illustration 1.3(b).  Upon application of pressure, the transition temperature of this material can be increased to well above 150 K.¹⁰  Currently, HgBa₂Ca₂Cu₃O₈ holds the record for highest transition temperature under both applied and ambient pressure conditions.

Superconductivity has also been found in many other novel chemical systems.  Indeed the phenomenon has been observed for the inorganic polymer, (SN)_x which has a transition temperature of 1.2 K.  This material is the only known polymeric superconductor.  There are also a number of crystalline organic superconductors made of charge-transfer salts, the most studied of which are based on the salts of the following two compounds:  tetramethyltetraselenafulvalene, TMTSF, and bis(ethylenedithia)tetrathiafulvalene, ET.  More recently, a number of fullerenes doped with metals into their interstitial sites have been found to be superconducting.  Fullerenes are spherical balls or tubes made up of five and six membered rings of carbon.  The most studied and easiest to prepare and purify is C₆₀.  This spherical carbon allotrope packs in a cubic close packed arrangement.  The packing motif leaves tetrahedral and octahedral holes that can be easily filled with alkali metals such as K, Na, or Cs as well as other cations without distortion of the lattice.  The first superconducting fullerene system was K₃C₆₀ with a transition temperature of 18 K.  The substitution with the highest transition temperature is currently Cs₂RbC₆₀ with a transition temperature of 33 K.

There are still many unexplored chemical systems in which superconductivity may exist.  One lesson that may be learned from the study of the cuprate system is that superconductivity may be found in ordered systems with many complex components and diverse chemical compositions.  Careful control of the chemical composition may be needed in the formation of new superconductors.