I'm looking for a pedagogic introduction to d-wave superconductivity.

Ideally, this would involve a derivation of d-wave superconductivity and the form of the gap parameter from some fundamental Hamiltonian (if such a derivation is even possible).

Books and papers are welcome.

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    $\begingroup$ rmp.aps.org/abstract/RMP/v67/i2/p515_1 and references therein $\endgroup$
    – wsc
    Oct 6, 2011 at 13:25
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    $\begingroup$ A derivation is the Big Question of the field, so that's going to be right out. You should give some details about what your background level it --- are you familiar with BCS theory? Eliashberg theory (and field theory in general)? Do you already understand the role of impurities (magnetic and not) in BCS theory? In the absence, I can recommend "Quantum Liquids" by Anthony Leggett, which contains an impartial evaluation of the phenomena and theories of cuprates near the end, and the rest of book contains everything else you need to understand it. $\endgroup$
    – genneth
    Oct 6, 2011 at 13:39
  • $\begingroup$ Thanks for the answers so far! I know about BCS theory (though not about impurities) and field theory (though from the hep perspective). I haven't heard about Eliashberg theory. $\endgroup$
    – Emerson
    Oct 6, 2011 at 18:37
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    $\begingroup$ also: rmp.aps.org/abstract/RMP/v72/i4/p969_1 $\endgroup$
    – Jen
    Oct 7, 2011 at 10:51

1 Answer 1


As has been said in the comment, there is no theoretical proof which validates $d$-wave pairing (or symmetry of the gap parameter) for the moment. But you can expand the order parameter to get higher angular momentum, and try to find the higher critical temperature associated to a given angular momentum.

More details can be found in the review

Sigrist, M., & Ueda, K. (1991). Phenomenological theory of unconventional superconductivity. Reviews of Modern Physics, 63(2), 239–311. http://dx.doi.org/10.1103/RevModPhys.63.239

Mineev, V. P., & Samokhin, K. (1998). Introduction to unconventionnal superconductivity. Gordon and Breach Science Publishers.

You can also try to find some experimental evidence for $d$-wave pairing. They usually involve some interference effect (also called phase sensitive or Josephson effect sometimes). These experiments are reviewed in the references already cited in the comment:

Van Harlingen, D. J. (1995). Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors—Evidence for dx2-y2 symmetry. Reviews of Modern Physics, 67(2), 515–535. http://dx.doi.org/10.1103/RevModPhys.67.515

Tsuei, C. C., & Kirtley, J. R. (2000). Pairing symmetry in cuprate superconductors. Reviews of Modern Physics, 72(4), 969–1016. http://dx.doi.org/10.1103/RevModPhys.72.969


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