S-wave and d-wave superconductivity

[FortranMan]

While there seems to be a general agreement that HTSCs are d-wave, I have heard from a few places that there is still a debate as to whether HTSCs are actually a mixture of s-wave and d-wave models. Is this true?

Also, what is meant by s-wave? Is the s-wave model the BCS model (with the s referring to the shape of the Fermi surface that the model deals with)? And if HTSCs are a combination of s-wave and d-wave, how do the two different models interact with each other? Is one model good at explaining SC behavior from Tc to T* while the other is good from T* to T = 0K? Do they work in tandem but differ across different fields?

 

[nbo10]

s-wave pairing has a isotropic energy gap. d-wave paring has nodes in the energy gap.

There is a review on pairing in the cuprates in Review on Modern Physics, 72, 696 "Pairing symmetry in cuprate superconductors"

 

[f95toli]

While there seems to be a general agreement that HTSCs are d-wave, I have heard from a few places that there is still a debate as to whether HTSCs are actually a mixture of s-wave and d-wave models. Is this true?

Yes, it is still being debatted. Although it seems clear that the admixture of s must be pretty small; less than 10%. Also, the evidence is ambigous and measurement that are often interpreted as showing signs of s-wave can also be explained using alternative models, generally imperfections in the samples (it is of course more complicated than that, but that is the essence of it).
Personally I am a sceptical; in most cases it seems the presence of a s-wave component is invoked in the discussion part of papers just to explain measurement data that the authors don't fully understand.

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Also, what is meant by s-wave? Is the s-wave model the BCS model (with the s referring to the shape of the Fermi surface that the model deals with)? And if HTSCs are a combination of s-wave and d-wave, how do the two different models interact with each other? Is one model good at explaining SC behavior from Tc to T* while the other is good from T* to T = 0K? Do they work in tandem but differ across different fields?

No, BCS har nothing to do with it. s-wave basically means that the gap (aka the order parameter) is isotropic wheras d-wave means that it has the shape of four lobes with alternating signs and nodes where the gap is zero inbetween these lobes.
When people talk about admixtures of s they mean that the gap has the shape of d+s or d+is (imaginary s); it basically means that the gap does not go to zero in the nodes but has some small value.
Hence, they are not two different models; it is ONE model but with several possible gap symmetries.

The review nbo10 refers to is good but it is quite old. There are quite a few things missing from it and a some things should be taken with a grain of salt. Tsuei certainly knew the topic very well, but the review was written at a time when it wasn't even quite clear that the HTS are really d-wave superconductors (at the time some people still thought it might be possible to explain most measurement using models based on a pure s-wave gap).

 

[FortranMan]

No, BCS har nothing to do with it. s-wave basically means that the gap (aka the order parameter) is isotropic wheras d-wave means that it has the shape of four lobes with alternating signs and nodes where the gap is zero inbetween these lobes.

I guess my understanding of BCS is bad, because from what I was studying I thought the main difference between BCS and d-wave theory was that the Fermi surface for BCS is isotropic while it's anisotropic for d-wave. What exactly is the difference between BCS and s-wave? I have a minimal understanding of how Cooper pairs are involved in BCS theory, but as far as I know they are involved in forming the energy gap. Are Cooper pairs at all involved in s-wave theory? Do the energy gaps in BCS and s-wave differ or does the mechanism that forms them differ?

When people talk about admixtures of s they mean that the gap has the shape of d+s or d+is (imaginary s); it basically means that the gap does not go to zero in the nodes but has some small value.
Hence, they are not two different models; it is ONE model but with several possible gap symmetries.

Have you ever read the paper by Harshman et al. "Nodeless pairing in single-crystal YBa 2 Cu3 O7." Phys. Rev. B, 69:174505, 2004? If so what were your thoughts on their study?

 

[ZapperZ]

I guess my understanding of BCS is bad, because from what I was studying I thought the main difference between BCS and d-wave theory was that the Fermi surface for BCS is isotropic while it's anisotropic for d-wave. What exactly is the difference between BCS and s-wave? I have a minimal understanding of how Cooper pairs are involved in BCS theory, but as far as I know they are involved in forming the energy gap. Are Cooper pairs at all involved in s-wave theory? Do the energy gaps in BCS and s-wave differ or does the mechanism that forms them differ?

The BCS theory is actually quite generic. It is just that in the original BCS theory, they applied it to the conventional superconductors with phonon mechanism. But there's nothing to prevent us from applying it to more exotic situation. It doesn't mean it is right, but it also doesn't mean it can't be done.

One of the things that I had done was to model the density of states of high-Tc superconductors that we found from tunneling spectroscopy. Since I did this during the "early" part of the history of high-Tc superconductors, we have no other means to do this than to apply BCS description but using d-wave gap symmetry and the appropriate band structure (i.e. the anisotropic fermi surface). We did this via calculating the single-particle spectral function within the mean-field approximation (which is what BCS assumes). When you do that, you can actually get quite reasonable agreement with the observed DOS, i.e. the sharp V-shaped gap rather than the flat-bottom gap that one gets from s-wave. For many years, this was the only way to extract any pertinent information from the DOS, such as the gap magnitude, and its temperature dependence. Yet, this is still BCS, technically.

So no. Having d-wave symmetry and anisotropic fermi surface does not rule out BCS.

Zz.

 

[nbo10]

Have you ever read the paper by Harshman et al. "Nodeless pairing in single-crystal YBa 2 Cu3 O7." Phys. Rev. B, 69:174505, 2004? If so what were your thoughts on their study?

Take everything from Harshman and company with extreme caution. They do some funny data analysis with the muon spin measurements and there maybe other "issues" as well.

 

[FortranMan]

funny you would say that, I'm kind of participating in that funny data analysis : )

As far as I can tell you from the inside, they're using E.H. Brandt's approximation for thermal variations in the vortex pinning, which allows them a greater number of parameters to fit the data, specifically YBCO in the project I was working on. Recently in the data analysis I was doing we had to make Tc field dependent using an empirical formula, and we dismissed one point as an outlier based on that formula, and from those twick we got a much better chi^2 for all the models we were comparing to the YBCO data. If you care to hear more let me know and I'll try to clear up this "funny business".

 

[nbo10]

Thats good to hear.

I'll make one suggestion, please explain your data analysis to your collaborator's. I've had discussion's with a few of 'em and all they can say is "taking into account vortex pinning, which no one else does, YBCO is without a doubt s-wave".

 

[ZapperZ]

Thats good to hear.

I'll make one suggestion, please explain your data analysis to your collaborator's. I've had discussion's with a few of 'em and all they can say is "taking into account vortex pinning, which no one else does, YBCO is without a doubt s-wave".

I'll even add to that and ask them to explain the zero-bias anomaly in tunneling data that can, so far, be explained with d-wave symmetry. For example, look at this:

J.Y.T. Wei et al, PRL 81, 2542 (1998)

which was done on YBCO.

Zz.

 

[nbo10]

I've asked similar questions, and the response boils down to "defects in the materials and/or if you do the analysis correctly you can fit the data to an s-wave model."

 

[ZapperZ]

I've asked similar questions, and the response boils down to "defects in the materials and/or if you do the analysis correctly you can fit the data to an s-wave model."

Tell them to either write a rebuttal to those papers, or publish their own analysis to account for the experiment. So that's what *I* would tell them in return before I tell them that their analysis isn't correct and there's defect in their material.

:)

Zz.

 

[f95toli]

I've asked similar questions, and the response boils down to "defects in the materials and/or if you do the analysis correctly you can fit the data to an s-wave model."

Thats nonsense. I spent several years doing transport measurements on high-angle (node-lobe transport) YBCO Josphson junctions and SQUIDs; there is NO WAY you can fit the data I (and others working on the same type of systems) obtained using an s-wave model. And yes I (and everyone else) DO take "defects" (faceting etc) into account when we analyze data; the faceting has a huge effect on the transport properties but can be modelle.. Moreover, the d-wave symmetry means that the facting give rise to a Jc(x) that can change sign as you move along the interface in high-angle junctions (0-45 in my case) which in turn affects everything from the current-phase relation to the types of vortices you get in long junctions (splinter vortices). s-wave superconductors (and even low angle YBCO Josephson junctions where the transport is lobe-lobe) are nowhere near as sensitive.

Also, all the scanning-SQUID measurements done by e.g. Kirtley and Tsuei on many different materials have shown evidence of phi_0/2 vortices; something that simply do not exist in s-wave superconductors. Read the review nbo10 recommended.

Finally, pi-junctions that use the intrinsic phase shift of d-wave have been around for several years now (and yes, it IS possible, albeti extremely difficult, to make pi-junction out of s-wave superconductors as well; but the mechanism is complettely different) and are now even being used in RSFQ.

And this is just the evidence from transport measurements (ZapperZ has already mentioned the ZBCP so I did not include that). As far as I know all recent measurements done by STM, ARPES etc are consistent with an order parameter that is predominantly d-wave.

I don't have a problem with people presenting data that does not agree with the "consensus", if data that was properly measured does not fit existing models we need to understand why. But saying that "we are right and everyone else is wrong" is just arrogant

 

[nbo10]

You can present data till you're blue in the face, they're just going to dismiss everything you say. It comes down to that they think the cuprate planes theory is complete wrong; anyone who believes that the cuprate planes SC have been duped by Cava. And they are going to present that they have evidence to support their claim.

I look at the literature. The only citations their publications receive are from inside the collaboration.

 

[ZapperZ]

You can present data till you're blue in the face, they're just going to dismiss everything you say. It comes down to that they think the cuprate planes theory is complete wrong; anyone who believes that the cuprate planes SC have been duped by Cava. And they are going to present that they have evidence to support their claim.

I look at the literature. The only citations their publications receive are from inside the collaboration.

Then we have nothing to worry about. They are just bitter.

Zz.

 

[FortranMan]

sorry for bringing this up again but I have a quick question. In Gerald Burns's Solid State Physics book, published in 1985, on page 650, he mentions that the following formula for a temperature dependent critical field formula

H_{c}=H_{0} [1-1.07(T/T_C)^2]

Was once empirical, but BCS theory has been comprehensive enough to prove it. Does the d-wave and mixed s-wave/d-wave theories also support this formula?