London equations

As a material drops below its superconducting critical temperature, magnetic fields within the material are expelled via the Meissner effect. The London equations give a quantitative explanation of this effect.

The London equations, developed by brothers Fritz and Heinz London in 1935,^[1] are constitutive relations for a superconductor relating its superconducting current to electromagnetic fields in and around it. Whereas Ohm's law is the simplest constitutive relation for an ordinary conductor, the London equations are the simplest meaningful description of superconducting phenomena, and form the genesis of almost any modern introductory text on the subject.^[2]^[3]^[4] A major triumph of the equations is their ability to explain the Meissner effect,^[5] wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold.

^ London, F.; London, H. (1935). "The Electromagnetic Equations of the Supraconductor". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 149 (866): 71. Bibcode:1935RSPSA.149...71L. doi:10.1098/rspa.1935.0048.
^ Michael Tinkham (1996). Introduction to Superconductivity. McGraw-Hill. ISBN 0-07-064878-6.
^ Neil Ashcroft; David Mermin (1976). Solid State Physics. Saunders College. p. 738. ISBN 0-03-083993-9.
^ Charles Kittel (2005). Introduction to Solid State Physics (8th ed.). Wiley. ISBN 0-471-41526-X.
^ Meissner, W.; R. Ochsenfeld (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". Naturwissenschaften. 21 (44): 787. Bibcode:1933NW.....21..787M. doi:10.1007/BF01504252. S2CID 37842752.

[1] London, F.; London, H. (1935). "The Electromagnetic Equations of the Supraconductor". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 149 (866): 71. Bibcode:1935RSPSA.149...71L. doi:10.1098/rspa.1935.0048.

[2] Michael Tinkham (1996). Introduction to Superconductivity. McGraw-Hill. ISBN 0-07-064878-6.

[3] Neil Ashcroft; David Mermin (1976). Solid State Physics. Saunders College. p. 738. ISBN 0-03-083993-9.

[Kittel-4] Charles Kittel (2005). Introduction to Solid State Physics (8th ed.). Wiley. ISBN 0-471-41526-X.

[5] Meissner, W.; R. Ochsenfeld (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". Naturwissenschaften. 21 (44): 787. Bibcode:1933NW.....21..787M. doi:10.1007/BF01504252. S2CID 37842752.

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