Two questions, really:
I’m finding it hard to wrap my head around the connections between k-space and real-space for d-wave symmetry, as well as the connections between “order parameter,” “gap,” “Cooper pair wave function,” and “superconducting wavefunction,” which are all mentioned above at various points in some of the other threads I have been looking through.
Right now I’m reading the article “The Case for d-wave pairing in the Cuprate Superconductors” by Doug Scalapino (1995), and am confused by Appendix B, which--at least from the tone of the appendix--should be pretty universally-agreed-upon stuff. The purpose of the appendix is to precisely explain what is meant by d-wave pairing. Scalapino writes at one point that:
“Physically, in a superconductor, the quasi-particles interact with the pair condensate so that the gap Δk in the quasi-particle spectrum is related to ψk [a notation for k-space amplitudes of the orbital wave function, which was earlier on described in real space]. The BCS theory tells us that
ψk = Δk / Ek.”
The same equality appears in other places, for example, Tsuei and Kirtley, RMP 72, 969 (2000), but so far, I haven't felt like I have gotten a sufficiently satisfactory explanation of its origin. Does anyone know where this equation comes from, how I might derive it, or better yet, how I might understand it intuitively? I have not (yet) been able to locate in the original BCS paper, or in Michael Tinkham’s book “Introduction to Superconductivity.”
Also, can anyone explain why, out of all the various quantities related to orbital symmetry, it is Δk that can be quantitatively written down as a “pure” d-wave, i.e., as
Δk = Δ0 [Cos(kx) – Cos(ky)]?
Thanks in advance.
I’m finding it hard to wrap my head around the connections between k-space and real-space for d-wave symmetry, as well as the connections between “order parameter,” “gap,” “Cooper pair wave function,” and “superconducting wavefunction,” which are all mentioned above at various points in some of the other threads I have been looking through.
Right now I’m reading the article “The Case for d-wave pairing in the Cuprate Superconductors” by Doug Scalapino (1995), and am confused by Appendix B, which--at least from the tone of the appendix--should be pretty universally-agreed-upon stuff. The purpose of the appendix is to precisely explain what is meant by d-wave pairing. Scalapino writes at one point that:
“Physically, in a superconductor, the quasi-particles interact with the pair condensate so that the gap Δk in the quasi-particle spectrum is related to ψk [a notation for k-space amplitudes of the orbital wave function, which was earlier on described in real space]. The BCS theory tells us that
ψk = Δk / Ek.”
The same equality appears in other places, for example, Tsuei and Kirtley, RMP 72, 969 (2000), but so far, I haven't felt like I have gotten a sufficiently satisfactory explanation of its origin. Does anyone know where this equation comes from, how I might derive it, or better yet, how I might understand it intuitively? I have not (yet) been able to locate in the original BCS paper, or in Michael Tinkham’s book “Introduction to Superconductivity.”
Also, can anyone explain why, out of all the various quantities related to orbital symmetry, it is Δk that can be quantitatively written down as a “pure” d-wave, i.e., as
Δk = Δ0 [Cos(kx) – Cos(ky)]?
Thanks in advance.
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