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Chapter 13. Superconductors and Superfluids

18th December 2017 by Dr Helen Klus

13.1 Discovery of superconductivity

Superconductivity is a macroscopic quantum effect that was first discovered by Dutch physicist Heike Kamerlingh Onnes in 1911.[1] Kamerlingh Onnes was studying the electrical resistance of mercury at low temperatures and found that at about 2 Kelvin (-267.15 °C) the resistance abruptly dropped to zero.

In ordinary conductors, electrical resistance lowers as the temperature decreases but it never reaches zero because the electrons collide with each other. Yet an electric current flowing in a loop of mercury wire could potentially maintain a current forever, with no applied voltage - although you would have to provide the energy to keep it cool - and so mercury was dubbed a superconductor.

13.1.1 The Meissner effect

Many other metals were found to act the same way and, in 1933, German physicists Walther Meissner and Robert Ochsenfeld showed that superconductors also expel magnetic fields.[2] This is known as the Meissner effect. The force of a superconductor’s magnetic field can be stronger than the gravitational force of some objects, allowing them to levitate.

13.1.2 Cooper pairs

In 1957, American physicists John Bardeen, Leon Cooper, and John Robert Schrieffer showed that superconductivity can be explained if, at low enough energies, electrons form a single quantum wave made of pairs of electrons with equal and opposite spins and momentums.[3,4] These are known as pair condensates, or Cooper pairs.

Electrons are normally repulsed by the negative charge of other electrons but, in 1956, Cooper had shown that sometimes electrons can overcome this repulsion and form bound pairs.[5] This happens when a stronger force attracts both electrons. In classical theories, this could be the charge of the positive ions within a conductive metal, but in the quantum case, it is due to the interaction of electrons with phonons. A phonon is the unit of energy that arises because the atoms within a metal are oscillating. These oscillations produce waves that carry heat and sound throughout the metal.

Photograph of a levitating tile.

Figure 13.1
Image credit

Superconducting levitation.

Photograph of a superfluid dripping out of  its container.

Figure 13.2
Image credit

A superfluid escaping its container.

When in pairs, the electrons - which are fermions with a spin value of 1/2 or -1/2 - act as if they have a spin value of 0, and so do not obey the Pauli exclusion principle. They tend to ‘condense’ into the lowest energy state, where their wave functions overlap and they act like one large atom or wave - a Bose Einstein condensate.

Cooper pairs are easily broken by thermal energy and so the temperature must be kept low. Bardeen, Cooper, and Schrieffer’s theory showed that materials could not become superconductive over about 30 Kelvin (-243.15 °C).

In 1986, however, German physicist Johannes Georg Bednorz and Swiss physicist Karl Alexander Müller discovered superconductivity in a ceramic material at 35 Kelvin (-238.15 °C).[6] Within a year, superconductivity was shown to occur at 93 Kelvin (-181.15 °C), which meant liquid nitrogen could be used as a coolant.[7]

Many other superconductors have since been found at temperatures as high as 138 Kelvin (-135.15 °C).[8] It’s still not understood how pair condensates form in these cases, although they may be created by waves formed by oscillating spin rather than oscillating atoms.[9]

Superconducting wires are currently used in a number of modern technologies. They help create the electro-magnets in MRI (Magnetic resonance imaging) scanners,[10] and are used to create high speed, magnetically levitated trains, known as Maglev trains.[11] There are currently Maglev trains in operation in South Korea and in Japan, which can reach speeds of up to 600 km/h (373 mph).[12]

Superconductivity can occur in protons as well as electrons. Protons are expected to form a superconducting fluid within the crust, and possibly the core, of neutron stars (discussed in Book I), which are expected to have temperatures of millions of Kelvin.[13] The critical temperature for superconductivity to occur is much higher in this case because protons interact via the strong nuclear force (discussed in Chapter 23) rather than the electromagnetic force (discussed in Chapter 22).[14]

13.2 Discovery of superfluidity

Superfluidity is a similar effect to superconductivity that was discovered by Canadian physicist John “Jack” Allen and British physicist Don Misener in 1937,[15] and was independently discovered by Russian physicist Pyotr Kapitza the same year.[16]

Superfluidity allows liquids to flow with zero viscosity, where viscosity is a measure of resistance, analogous to electrical resistance. This allows them to stay completely still even if their container is rotating, flow through pores in their containers, and flow vertically upwards. This occurs because of the siphon effect, which is possible because they still have water tension.

Superfluids are formed in two ways:

  • If the fluid is composed of bosons - like helium-4 - it becomes a real Bose Einstein condensate.
  • If it is composed of fermions - like helium-3 or neutrons - then it can imitate a Bose Einstein condensate.

A superfluid composed of fermions imitates a Bose Einstein condensate in the same way that electrons imitate bosons when the exhibit the effects of superconductivity. In superfluidity however, the pairs can be formed from neutral atoms or particles, and the interaction is mediated by waves caused by oscillating spin. Superfluidity can occur at higher temperatures in fluids made of bosons, but the superfluid state is destroyed if the fluid moves over a certain critical velocity.

Superfluidity, like superconductivity, is thought to exist inside neutron stars.

13.3 References

  1. Kamerlingh Onnes, H., Proceedings of the Koninklijke Akademie van Wetenschappen te Amsterdam 1911, 14, 113–115.

  2. Meissner, W., Ochsenfeld, R., Naturwissenschaften 1933, 21, 787–788.

  3. Bardeen, J., Cooper, L. N., Schrieffer, J. R., Physical Review 1957, 106, 162–164.

  4. Bardeen, J., Cooper, L. N., Schrieffer, J. R., Physical Review 1957, 108, 1175–1204.

  5. Cooper, L. N., Physical Review 1956, 104, 1189–1190.

  6. Bednorz, J. G., Müller, K. A., Zeitschrift für Physik B Condensed Matter 1986, 64, 189–193.

  7. Wu, M. K., Ashburn, J. R., Torng, C., Hor, P. H., Meng, R. L., Gao, L., Huang, Z. J., Wang, Y. Q., Chu, A., Physical Review letters 1987, 58, 908–910.

  8. Dai, P., Chakoumakos, B. C., Sun, G. F., Wong, K. W., Xin, Y., Lu, D. F., Physica C 1957, 243, 201–206.

  9. Radovan, H. A., Fortune, N. A., Murphy, T. P., Hannahs, S. T., Palm, E. C., Tozer, S. W., Hall, D., Nature 2003, 425, 51–55.

  10. Filippi, M., Stefano, N. de, Dousset, V., MR Imaging in White Matter Diseases of the Brain and Spinal Cord, Springer Science & Business Media, 2005.

  11. Liu, Z., Long, Z., Li, X., Maglev Trains: Key Underlying Technologies, Springer, 2015.

  12. McCurry, J., Japan’s maglev train breaks world speed record with 600km/h test run, The Guardian, 2015.

  13. Shternin, P. S., Yakovlev, D. G., Heinke, C. O., Ho, W. C. G., Patnaude, D. J., Monthly Notices of the Royal Astronomical Society: Letters 2011, 412, 108–112.

  14. Cartlidge, E., Neutron star has superfluid core, Physics World, 2011.

  15. Allen, J. F., Misener, A. D., Nature 1938, 141, 75.

  16. Kapitza, P., Nature 1938, 141, 74–75.

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How We Came to Know the Cosmos: Light & Matter

I Pre 20th Century theories

1. Atoms and Waves

2. Reflection, Refraction, and Diffraction

3. Newton's theory of Light

4. Measuring the Speed of Light

5. 19th Century Wave Theories

6. 19th Century Particle Theories

7. Spectral Lines

II Quantum Mechanics

8. Origin of Quantum Mechanics

9. Development of Atomic theory

10. Quantum Model of the Atom

11. Sommerfeld's Atom

12. Quantum Spin

13. Superconductors and Superfluids

14. Nuclear Physics

15. De Broglie's Matter Waves

16. Heisenberg's Uncertainty Principle

17. Schrödinger's Wave Equation

18. Quantum Entanglement

19. Schrödinger's Cat

20. Quantum Mechanics and Parallel Worlds

III Quantum field theories

21. The Field Concept in Physics

22. The Electromagnetic Force

23. The Strong Nuclear Force

24. The Weak Nuclear Force

25. Quantum Gravity

IV Theories of the mind

26. Mind-Body Dualism

27. Empiricism and Epistemology

28. Materialism and Conscious Matter

29. Material theories of the Mind

30. Material theories of the Mind vs. Descartes

31. The Mind and Quantum Mechanics

32. The Limitations of Science

V List of symbols

33. List of symbols

34. Image Copyright