Superconductivity. 24 February Paul Wilson Tutor: Justin Evans

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1 Superconductivity 24 February 2009 Paul Wilson Tutor: Justin Evans 1

2 Intended Audience This report is intended for anyone wishing to understand the fundamentals of superconductors and their growing importance in modern science and engineering. Summary Superconductors exhibit negligible resistance at low temperatures There are two types of superconductor: low temperature (type 1) and high temperature (type 2) BCS Theory explains low temperature superconductors in terms of cooper-pairs of electrons No theory currently exists to adequately explain high temperature superconductors A major goal is to find a material that is superconductive at room temperature Superconductors have major applications in computer circuitry, medical scanning and magnetic levitation transport What is superconductivity? Numerous cryogenic experiments in the late 19 th and early 20 th centuries showed that if a substance was cooled its capacity to conduct electricity increases in proportion to the reduction in temperature, something already known to be a consequence of reducing the resistance according to Ohm s law. The relationship drawn from these observations led to notable figures in the field such as Dewar and Fleming postulating that there should be immeasurable resistance at absolute zero. In pursuit of an answer, and with the appropriate equipment at his disposal, in 1911 Heike Kamerlingh Onnes was the first to discover the superconducting properties of mercury at a temperature of 4.2K. Far from a simple linear decline to absolute zero, it was clear that for some special substances the resistance reduces linearly with temperature until a certain point, known as the critical temperature, at which there is an abrupt decrease to almost no measurable electrical resistance (see figure 1); it was not long before many other substances were also tested to see whether cooling had the same effect. It followed from this, and was widely expected, that removing the power supply to a currentcarrying superconductor would result in the current continuing to flow without diminishing in energy, a theory which was experimentally verified by Onnes in

3 How does it work? Figure 1 - Onnes' original resistance vs. temperature graph for Mercury There are currently two classes of superconductor; the low temperature superconductors, which can be explained by BCS theory, and high temperature superconductors, for which there is currently no universally agreed-upon explanation. For this reason the latter class is an area of highly active research. An important step in understanding superconductors came from the work of Meissner and Oschenfeld, who observed that above the critical temperature a magnetic field can penetrate the material, but below the critical temperature the field is totally excluded by the surface currents induced on the superconductor and no flux penetrates the interior (see figure 2). One well known example of this phenomenon can be seen in various popular science videos of magnets floating above liquid-nitrogen cooled superconductors. If a sufficiently strong magnetic field is used then the superconducting properties of the material may be destroyed and the material will no longer repel the field. 3

Figure 2 - The Meissner effect on a superconductor above and below the critical temperature BCS theory was formulated by John Bardeen, Leon Cooper and John Schrieffer in 1957 and successfully

4 Figure 2 - The Meissner effect on a superconductor above and below the critical temperature BCS theory was formulated by John Bardeen, Leon Cooper and John Schrieffer in 1957 and successfully explains how superconductivity works for metals below around 77K. In this theory electrons distort the lattice structure of the metal through which it is travelling, creating a potential well which affects the electron directly following it so that the current is carried by bound pairs of electrons, known as cooper pairs. The momentum of the cooper pair is not changed throughout this process, resulting in a current that flows unimpeded for an indefinite amount of time. However, the energy maintaining the Cooper pairs is quite weak and can be broken up easily with the addition of thermal energy. So only at low temperatures are a significant number of the electrons in a metal in Cooper pairs, thus making this an idea which fitted observed data but which would not work if superconductivity was found to happen at higher temperatures, something which appeared to be inevitable given the continually rising critical temperatures found in all subsequent superconductor experiments. New discoveries of high temperature superconductivity In 1986 scientists from IBM discovered superconducting properties of materials with critical temperatures above 77K, the so-called high temperature superconductors. These materials and subsequent similar ones were often ceramics, large compounds and alloys and behaved in ways that could not be explained by BCS theory. At low temperatures, the laws of quantum mechanics take precedence over classical theories and just as in more familiar circumstances with changes of state in liquids and gases there is a phase transition when the material can change abruptly from one state to another. This collective behaviour at the atomic scale can also be applied to superconductivity and the analogous changes observed at the critical temperature. 4

5 Figure 3 - Graph showing resistance vs. temperature for two high-temperature superconductors In these models proposed to describe the material structure there is a global change in behaviour of the superconductor due to the local, short-range interactions of the electrons with the positively charged lattice resulting in sudden phase changes from stable states. However, this does not appear to be the case for high-temperature superconducting materials. Current knowledge and uses of superconductors Superconductivity is known to occur in 26 metallic elements and in many compounds and alloys although no unified theory has been produced to explain the phenomenon at high temperatures. Currently, superconductors can produce some of the most powerful electromagnets which can be used in a wide range of fields including magnetic resonance imaging (MRI) in hospitals, so that patients do not have to be exposed to radiation, to guiding beams around particle accelerators. Mass spectrometry also makes use of the powerful electromagnets afforded by superconductivity. Superconductor (Chemical formula) Critical Temperature (approx.) / K (Sn 5 In)Ba 4 Ca 2 Cu 11 O y 218 (Sn 5 In)Ba 4 Ca 2 Cu 10 O y 212 Sn 6 Ba 4 Ca 2 Cu 10 O y 200 (Sn 1.0 Pb 0.5 In 0.5 )Ba 4 Tm 6 Cu 8 O (Sn 1.0 Pb 0.5 In 0.5 )Ba 4 Tm 5 Cu 7 O Table 1 - Current highest temperature superconductors, all large-compound cuprates Future applications of superconductivity The ultimate goal of superconductor research is to find a material which behaves as a superconductor at room-temperature (293K). This would have profound effects on industry 5

6 and technology, where magnetic levitation vehicles such as trains will be able to travel faster and more efficiently with greatly reduced friction; superconductors may become an efficient way of storing power due to the way in which a current may flow unimpeded indefinitely. However, engineering these will be more difficult to achieve for devices which do not use direct currents, due to the fact that an alternating current can disrupt the magnetic field around the superconductor. It is highly likely that superconductors will eventually replace traditional conductors and improve efficiency and save money. References [1] John Daintith et al., Dictionary of Physics, Oxford University Press (2005) [2] Jewett, Serway, Physics for scientists and Engineers, Thomson (2007) [3] Philip Ball, Critical Mass, Arrow Books (2007) [4] [5] "On the sudden change in the rate at which the resistance of mercury disappears". Comm. Leiden. 25 Nov, (1911) [6] W. Meissner and R. Oschenfeld, Naturwiss. 21, 787 (1933) [7] J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957) [8] Figure [9] Figure [10] Figure

Superconductors. An exciting field of Physics!

Superconductors. An exciting field of Physics! Superconductors An exciting field of Physics! General Objective To understand the nature of superconductivity Specific Objectives: You will be able to 1. Define Superconductivity 2. State the history of