Superconductivity by Blundell Stephen J.;

Author:Blundell, Stephen J.;
Language: eng
Format: epub
Publisher: Oxford University Press
Published: 2009-03-14T16:00:00+00:00

20. Superconducting order appears below the critical temperature

In the circuit, ground is at zero volts. However, since in circuits you only ever measure ‘potential differences’, it would be quite possible (though perverse) to redefine ‘ground’ to be 40,000 Volts and have all the other voltages in the circuit defined with respect to that. This looseness in the description of electricity (the fact that you can define the electrical ground to be whatever you like) is an example of gauge symmetry. To preserve this symmetry, Ginzburg and Landau had to write down their equations in a particular way. When they did this, they ended up with a pair of rather complicated differential equations for the quantity ψ, but very encouragingly they found that the solutions of these equations obligingly spit out the London equations, the penetration depth and the coherence length, in other words a whole lot of physics that had taken a couple of decades for others to formulate.

Because their theory was phenomenological, the charge of the superconducting carrier, which they called e*, could be taken to be anything. Landau didn’t see why it should be any different from the charge of the electron e, so in the paper they explicitly wrote ‘there are no grounds to believe that the charge e* is different from the electron charge’. Five years later, Ginzburg realized that agreement with experimental data could be achieved if they took e* as somewhere around twice or three times the electronic charge.

Landau was not convinced and advanced an argument that the beautiful ‘gauge invariance’ of their theory would fall apart if e* was taken to be anything other than e. In the event, it turned out from the BCS theory that, because of the pairing of electrons, the charge of the superconducting carrier was precisely twice the electronic charge. Furthermore, the BCS theory showed how the ‘gauge invariance’ of the theory could be maintained. As Ginzburg put it later, ‘Landau was right in the sense that the charge e* should be universal and I was right in that it is not equal to e. However, the seemingly simple idea that both requirements are compatible and e* = 2e occurred to none of us.’ He also lamented that he did not see the solution that Bardeen, Cooper, and Schrieffer had so clearly grasped.

Nevertheless, Lev Gor’kov showed in 1959 that the Ginzburg-Landau equations could be derived from the BCS theory, and the Ginzburg–Landau approach is much less unwieldy for deriving important aspects of superconductivity. For Landau’s many achievements, he was awarded the Nobel Prize in 1962. Unfortunately, he was not able to collect it. Earlier that year, a car accident on an icy road between Moscow and Dubna left him in a coma for several months and he never properly recovered, dying six years later. Ginzburg had to wait a very long time for his Nobel recognition; aged 87, he collected the prize in 2003.

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