Abstract
Superconductivity was introduced in Chapter 26 of the previous volume. It was shown there that the unusual electrodynamic properties of superconductors are accompanied by anomalous thermodynamic behavior. After the presentation of some experimental results a phenomenological description was given using the London equations and the Ginzburg–Landau equations. Now that we have acquainted ourselves with the microscopic theory of some broken-symmetry phases, we return to the theory of superconductivity and attempt to give a microscopic description of this particular state of matter.
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Notes
- 1.
A pair with different symmetry should be found in the superfluid phase of 3He. Since the helium atoms cannot overlap, the spatial part of the wavefunction has to be antisymmetric and the spin part is a symmetric triplet.
- 2.
At zero temperature electrons with energy \(\xi_{{\boldsymbol{k}}} = \varepsilon_{{\boldsymbol{k}}}- \varepsilon_{\textrm{F}}\) contribute a term to the T-matrix which is proportional to \(\ln \xi_{{\boldsymbol{k}}}\). It diverges logarithmically as the energy of the scattered electrons approaches the Fermi energy.
- 3.
See page 4 in Volume 1.
- 4.
N. N. Bogoliubov, 1958, J. G. Valatin, 1958.
- 5.
A. P. Levanyuk, 1959, V. L. Ginzburg, 1960.
- 6.
N. N. Bogoliubov, 1958, P. G. De Gennes, 1966. Pierre-Gilles de Gennes (1932–2007) was awarded the Nobel Prize in 1991 “for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers
- 7.
A. F. Andreev, 1964. An electron approaching the normal–superconductor interface from the normal side with wave vector \({\boldsymbol{k}}\) is unable to penetrate deep into the superconductor if its energy measured from the chemical potential is smaller than the gap in the superconductor. It can be specularly reflected from the interface. Alternatively, the incident electron together with another electron of momentum \(-{\boldsymbol{k}}\) can penetrate into the superconductor to form a Cooper pair there. The electron with \(-{\boldsymbol{k}}\) missing from the normal side can be interpreted as a reflected hole with wave vector \({\boldsymbol{k}}\). It retraces the path of the incident electron.
- 8.
L. P. Gorkov, 1959, Y. Nambu, 1960.
- 9.
A. B. Migdal, 1958.
- 10.
W. L. McMillan, 1968.
- 11.
Whether these materials behave as Luttinger liquids in the anomalous metallic phase could not be proved beyond doubt experimentally.
- 12.
We will see in Chapter 35 that the phase diagram of the two-dimensional Hubbard model has similar features to the phase diagram discussed here. This model is, however, too simplified to capture the physical reality of these systems.
- 13.
The coexistence of antiferromagnetism and superconductivity is not excluded, since the coherence length, the spatial extension of the Cooper pairs, is typically much larger than the spatial periodicity of the antiferromagnetic order or the wavelength of the spin-density wave.
- 14.
The Josephson effect related to the supercurrent between superconducting electrodes was discussed in Chapter 26.
- 15.
The effective two-particle interaction V does not occur in the rest of this chapter, V denotes the voltage.
- 16.
As mentioned before, we are not considering the case when magnetic impurities are present in the insulating layer.
- 17.
MIM stands for metal–insulator–metal. The notation NIN for normal(metal)–insulator–normal(metal) is also used.
- 18.
V. Ambegaokar and A. Baratoff, 1963.
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Sólyom, J. (2010). Microscopic Theory of Superconductivity. In: Fundamentals of the Physics of Solids. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04518-9_7
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