Theory of Dirty Superconductors

August 15, 2024 Jeremiah Hendren

Theory of Dirty Superconductors

Anderson, Philip W.
Journal of Physics and Chemistry of Solids 11, no. 1-2 (1959): 26-30
https://doi.org/10.1016/0022-3697(59)90036-8

One of the most striking experimental facts about superconductivity is that it is often insensitive to enormous amounts of physical and chemical impurities. For one example, several substances in essentially an amorphous state have been shown to be superconductors, such as bismuth and beryllium films laid down at liquid-helium temperatures.1 As another example, there are disordered alloy systems with 20–50 per cent of chemical scattering centers, but with transition temperatures comparable with those of pure elements.2 These quantities of crystal imperfections are large enough to scatter the electrons at an extremely rapid rate. In fact, if we were to take the mean free time before scattering for the electron as a measure of the electrons’ uncertainty in energy, that uncertainty in energy is large compared not only with the energy gap ϵ0, but with the Debye energy ħwD. Plane-wave states for the electrons definitely have this very large degree of energy uncertainty.

P.W. Anderson

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