What Is D-Wave Superconductivity?

[kanato]

Can anyone explain or give online references that give some explanation of what d-wave superconductivity is? My (poor) understanding of it is limited to the symmetry of the gap in the first brillouin zone is such that there are 4 nodes. But does that mean there are places where the gap is negative? And what does that even mean, to have a negative gap (energy must be invested to create a pair??) ?

 

[ZapperZ]

Can anyone explain or give online references that give some explanation of what d-wave superconductivity is? My (poor) understanding of it is limited to the symmetry of the gap in the first brillouin zone is such that there are 4 nodes. But does that mean there are places where the gap is negative? And what does that even mean, to have a negative gap (energy must be invested to create a pair??) ?

It is similar to the $d_{x^2-y^2}$ symmetry of an orbital angular momentum. So it isn't something mysterious.

What it does mean is that you get nodes along the diagonal directions. And no, you don't get negative gap, because the gap measurement (as in tunneling) only measure the absolute value. These measurements are not phase sensitive.

Zz.

 

[kanato]

It is similar to the $d_{x^2-y^2}$ symmetry of an orbital angular momentum. So it isn't something mysterious.

What it does mean is that you get nodes along the diagonal directions. And no, you don't get negative gap, because the gap measurement (as in tunneling) only measure the absolute value. These measurements are not phase sensitive.

Zz.

So d-wave is referring to the gap then, and not say, the wave function of the cooper pair.

I guess I don't know what to ask to broaden my understanding about the subject about high Tc superconductors. What else is known about high Tc's that is different from superconductors which are described well by BCS or Eliashberg theory?

 

[ZapperZ]

So d-wave is referring to the gap then, and not say, the wave function of the cooper pair.

Actually, no. The symmetry refers to the "order parameter" as used in the Ginzburg-Landau theory. This phrase stuck through all of superconductivity and used in the BCS theory. The gap symmetry come out of this order parameter. This is not the same as the BCS ground state wavefuction (at least not entirely).

I guess I don't know what to ask to broaden my understanding about the subject about high Tc superconductors. What else is known about high Tc's that is different from superconductors which are described well by BCS or Eliashberg theory?

I wrote in a thread before on some issues surrounding high-Tc superconductors. See if this might answer some of your questions.

https://www.physicsforums.com/showthread.php?t=107083

Zz.

 

[siddharth]

I guess I don't know what to ask to broaden my understanding about the subject about high Tc superconductors. What else is known about high Tc's that is different from superconductors which are described well by BCS or Eliashberg theory?

Gokul gave a nice link on the http://physicsweb.org/articles/world/13/2/8/1#pw-13-02-08fig1". You might want to take a look at that.

 

[kanato]

Thanks for the links. I will read those.

 

[FortranMan]

While I was researching the superconductor YBCO and the BCS and d-wave models at William and Mary College, I came across a statement in a book that said that if high-temperature superconductors were d-wave, then room temperature superconductivity or superconductors with higher critical temperatures would be physically impossible.

Unfortunately that statement wasn't important in my research at the time so I didn't note down the source, but now that I based my senior project around it, I'd really like to know the name of that book. Has anyone heard this statement any where, in what source, and do you believe this statement carries any sort of credence? Does anyone know whether antiferromagnetic orientations are involved in this statement?

 

[f95toli]

While I was researching the superconductor YBCO and the BCS and d-wave models at William and Mary College, I came across a statement in a book that said that if high-temperature superconductors were d-wave, then room temperature superconductivity or superconductors with higher critical temperatures would be physically impossible.

Unfortunately that statement wasn't important in my research at the time so I didn't note down the source, but now that I based my senior project around it, I'd really like to know the name of that book. Has anyone heard this statement any where, in what source, and do you believe this statement carries any sort of credence? Does anyone know whether antiferromagnetic orientations are involved in this statement?

I can't see how anyone can make such a statement with any confidence. Since we don't understand WHY d-wave superconductors become superconducting in the first place it is impossible to say anything about an upper limit for Tc.
Remember that many people assumed that the maximum Tc for a conventional superconductor was just over 20K until MgB2 came along...

 

[Gokul43201]

While I was researching the superconductor YBCO and the BCS and d-wave models at William and Mary College, I came across a statement in a book that said that if high-temperature superconductors were d-wave, then room temperature superconductivity or superconductors with higher critical temperatures would be physically impossible.

Unfortunately that statement wasn't important in my research at the time so I didn't note down the source, but now that I based my senior project around it, I'd really like to know the name of that book. Has anyone heard this statement any where, in what source, and do you believe this statement carries any sort of credence? Does anyone know whether antiferromagnetic orientations are involved in this statement?

Could it be Cohen & Anderson, Superconductivity in d- and f- band metals (AIP, New York, 1972)?

There was mention of something very similar in a thread here, last year.

Incidentally, Anderson is in the next building at this very moment (probably eating lunch) - he gave a talk here this morning as part of a conference on Conductor-Insulator Transitions.

 

[ZapperZ]

Could it be Cohen & Anderson, Superconductivity in d- and f- band metals (AIP, New York, 1972)?

There was mention of something very similar in a thread here, last year.

Incidentally, Anderson is in the next building at this very moment (probably eating lunch) - he gave a talk here this morning as part of a conference on Conductor-Insulator Transitions.

So, did he manage to seduce you and a bunch of people into his RVB theory? :)

Zz.

 

[Gokul43201]

I think there are already a bunch of people that think there may be something - if not the Holy Grail - in RVB. The only overwhelming opinion seemed to be in relation to the pseudogap in the underdoped cuprates - the consensus seemed to be strongly favoring a view of precursor pairing over a model of competing orders. When Randeria was giving a review of the recent work in the field during his talk, the session chair even joked that he (Randeria) would not be allowed much time to talk about competing orders - I was pretty shocked to hear that!

 

[f95toli]

Could it be Cohen & Anderson, Superconductivity in d- and f- band metals (AIP, New York, 1972)?

I guess it might be good to point out that superconductivity in d-band metals has absolutely nothing to do with d-wave superconductivity.
There are several interesting d-band metals (Sc, Y etc) are superconducting but they are all BCS-superconductors. The "d" here refers to properties of the ATOMS.
The "d" in d-wave superconductivity refers to the symmetry of the superconudcitng wavefunction(aka the order parameter).

Both ZapperZ and Gokul43201 knows this, but I guess it might not be so obvious to people not familiar with high-Tc.

Anyway, a few years ago I heard Anderson give a talk where he was quite enthusiastic about some (then recent) numerical first-principles calculations. I don't remember the details or which material they were modeling but it looked interesting; is he still talking about this?
Last time I hear Anderson give a talk he was talking about something non-SC.

 

[Gokul43201]

Anderson is always enthusiastic about anything he does. I imagine he is no less enthusiastic today than he was 35 years ago, when he predicted an upper bound to Tc of about 30K (this was before HTSC, as f95 points out) or 50 years ago, when he developed localization theory. He is currently working on (amongst other things) explaining the weirdness of the underdoped cuprates. He has shown that there is a new vortex fluid phase within the pseudogap phase, where energy/entropy is carried by mobile vortices. This explains the recent Nernst effect experimental results, but does not in any way tie into the behavior of the pseudogap state itself.

 

[FortranMan]

I can't see how anyone can make such a statement with any confidence. Since we don't understand WHY d-wave superconductors become superconducting in the first place...

I am confused in how you are using the term "d-wave". From my understanding it is a new theoretical model (that has some extensions off of the BCS model) that would be able to microscopically describe vortex pinning behavior in type-II superconductors, and thus could be extended to predict higher order behaviors like maximum Tc values. However you use the term as if it is a given characteristic of type-II superconductors. Are all type-II superconductors "d-wave" superconductors? Is there already a consensus that the pairing in type-II superconductors is d-wave? Or are you just referring to the Fermi surface of type-II superconductors which seem to be generally d-wave in shape?

Mind you that I'm still exploring the subject if I am making any incorrect statements.

Remember that many people assumed that the maximum Tc for a conventional superconductor was just over 20K until MgB2 came along...

Was that upper limit prediction made with BCS theory? I'm assuming people made that prediction off of theoretical, microscopic models as opposed to the phenomenological two-fluid model. Oddly I think I remember the book I am looking for mentioning that it was actually the BCS model that was predicting higher Tc values than the d-wave model for type-II superconductors. Were people not taking into consideration Abrikosov vortices at the time?

Also are you implying that no microscopic model for type-II superconductivity can make upper limit predictions on Tc values?

Could it be Cohen & Anderson, Superconductivity in d- and f- band metals (AIP, New York, 1972)?

I have with me the AIP conference edition, but by the date alone I could tell this wasn't the book I was looking for as YBCO wasn't even discovered then. The print and cover also are unfamiliar to me. For some reason I feel the book I am looking for is more like the book edited by S.-L. Drechsler and T. Mishonov called "High-Tc Superconductors and Related Materials" (Kluwer, Dordrecht, 2001).

 

[f95toli]

I am confused in how you are using the term "d-wave". From my understanding it is a new theoretical model (that has some extensions off of the BCS model) that would be able to microscopically describe vortex pinning behavior in type-II superconductors, and thus could be extended to predict higher order behaviors like maximum Tc values. However you use the term as if it is a given characteristic of type-II superconductors. Are all type-II superconductors "d-wave" superconductors? Is there already a consensus that the pairing in type-II superconductors is d-wave? Or are you just referring to the Fermi surface of type-II superconductors which seem to be generally d-wave in shape?

When I talk about d-wave I am talking about the order parameter in high-Tc superconductprs such as YBCO, Bi-2212 etc. That the order parameter in YBCO has a d-wave symmetry was suggested quite soon after it was discovered but it took several years before it was shown that this was indeed correct (some people still think there is an admixture of s-wave there are as welll, but I am sceptical).
Now, all high-Tc superconductors are type-II supercondictors but "type I" and "type II" has in itself nothing directly to do with neither the critical temperature nor the order parameter. Most conventional superconductors are also type-II, e.g. niobium is often used in applications and is strongly type II.

Was that upper limit prediction made with BCS theory? I'm assuming people made that prediction off of theoretical, microscopic models as opposed to the phenomenological two-fluid model.

I don't think there is an upper limit as such, it just get "harder and harder" to create a condensate. BCS theory will give you the right value for Tc of MgB2 and the values for the two gaps assuming you know how to do the calculation (it can only be done numerically, but I am told it is straightforward using DFT).

There is a 'simple' formula developed by McMillan (but based on BCS) that can be used to predict Tc. This formula predicts a maxmum Tc of about 20K for a BCS superconductor I remember correcty. However, it is only valid under certain circumstances (some limiting cases), Mcmillan knew this and pointed it out in his paper, but that fact was somehow lost over the years and many people ended up assuming that 20K was the real limit.

Also, note that the high-Tc superconductors are notBCS superconductors. This has been known for a long time. Hence, neither the McMillan formula nor the full BCS formalism can be used to calculate e.g. the Tc of YBCO.

Edit: I just realized that I should perhaps mention that "order parameter" means the same thing as "superconducting wavefunction" in this context, i.e. it does not refer to the GL-parameter (which is just a numerical value and has nothing to do with the symmetry).