How is 3D d-wave superconductivity band?

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Discussion Overview

The discussion revolves around the nature of d-wave superconductivity, particularly focusing on the symmetry of the pairing function in relation to the z-axis and its representation in momentum space. Participants explore the implications of this symmetry in the context of cuprate superconductors.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents an image related to d-wave superconductivity and questions whether the symmetry is consistent along the z-axis or varies significantly.
  • Another participant asserts that in cuprate materials, the pairing function is constant along the z-axis, emphasizing the importance of momentum space representation.
  • A participant specifies that the symmetry in question is d_{x^2-y^2} and suggests that this can be verified in atomic spectroscopy literature.
  • A later reply reiterates the d_{x^2-y^2} symmetry but notes that atomic orbitals, being spherical harmonics, exhibit different z-axis symmetry, leading to a discussion about the shape of lobes and their representation in Brilliouin zones.

Areas of Agreement / Disagreement

Participants express some agreement on the identification of the d_{x^2-y^2} symmetry, but there is uncertainty regarding the implications of this symmetry along the z-axis and how it relates to atomic orbitals and Brilliouin zones. The discussion remains unresolved with competing views on the nature of the lobes and their representation.

Contextual Notes

There are limitations regarding the assumptions made about the symmetry and its representation, as well as the dependence on definitions related to atomic orbitals and their shapes. The discussion does not resolve these complexities.

MTd2
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Please,

I found this (the 4 lobe object in the center):
http://www.physics.utoronto.ca/lecture-and-seminar-series/colloquium/events/tsuei.jpg

But is it the same throughout the z axis, or does it vary significantly?
 
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I assume this is a description of the d-wave superconductivity as found in the cuprates. In those materials, there is a very prominent layered structure. So yes, along the z-axis the pairing function is constant. Remember however that you're looking at the pairing function in the momentum/Fourier-transformed space.
 
Or to be more specific, it is the [itex]d_{x^2-y^2}[/itex] symmetry. So if you open any atomic spectroscopy book, look up that orbital symmetry and there you have it.

Zz.
 
ZapperZ said:
Or to be more specific, it is the [itex]d_{x^2-y^2}[/itex] symmetry. So if you open any atomic spectroscopy book, look up that orbital symmetry and there you have it.

Zz.

Though atomic orbitals are spherical harmonics, so have a slightly different z-axis symmetry. In this case, the "lobes" should be open, so that concatenating Brilliouin zones creates a sort of "sausage". Otherwise, yes, it's called [itex]d_{x^2-y^2}[/itex], but only because its x-y plane symmetry has the same nodes (I'd like to say the same shape in general, but am not sure?)
 

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