# BCS theory

1. Jul 26, 2009

### Mentallic

I'm unsure where this is meant to go precisely, so if needed, move this thread where necessary.

Our class just touched up just slightly on BCS theory. We were told that conventional superconductors (SC) with Tc<30K were explainable by this theory, while unconventional SC's with Tc>30K couldn't be explained by BCS.

My question is - and sorry for the inappropriate nature of it - while the unconventional SC's can be explained by some other theory (I'm assuming) does this mean that it is fairly possible that neither BCS nor this other theory are truly correct? By my logic, there should be one theory that can explain all types of SC's.

2. Jul 26, 2009

### maverick_starstrider

Well no, superconductors are often divided into two classes "conventional" and "unconventional". I'm not an expert in superconductivity but let me see if I can illuminate a little. Now, if you basically take any metal and get it cold enough (usually some fraction of a degree above absolute zero, i.e. extraordinarily cold) you get a conventional superconductor. This superconducting state is understood to originate from electron-phonon coupling and is detailed by BCS theory. However, in 1986 it was discovered that certain compounds (i.e. not just a pure metal) also entered a superconducting state but at a significantly higher temperature. The first of these discovered, and to this day the most research by far, are the cuprates. However, in the ensuing years other "unconventional" superconductors have been found, most recently and importantly the iron pnictides. So why are these "unconventional"? Well because these compounds enter a superconducting state (one where their electric resistance is zero and they are perfectly diamagnetic), albeit an all together different state then the conventional superconductors, at a much higher temperature and the origin of this state does NOT Seem to be due to electron-phonon coupling. Now we still don't know how this superconducting state comes to be in unconventional superconductors (it'd take forever to go over what we do know, conduction confined to interlaced 2-d planes, etc.) however these unconventional superconductors are the really interesting ones because the transition temperature of conventional superconductors is so prohibitively low (you have to freeze them to less then a kelvin for most) that it makes them most useless for the vast majority of potential applications. However, there is hope that if we can understand the unconventional superconductors we can create compounds that entering a superconducting phase at above 77K (or, the holy grail is at room temperature). The 77K goal is because that is the temperature of liquid nitrogen which is SIGNIFICANTLY cheaper and easier to use then liquid helium (which is at like 3K or something I think) which must be currently used to put a superconductor in a superconducting state.

3. Jul 26, 2009

### xepma

To put it brief: the superconductivity is caused by the presence of Cooper pairs - bound states of the electrons. These Cooper pairs condense, and it is this condensation which is the cause of the superconductivity. It's important to realise that as long as you have Cooper pairs and they are in a condensed state, you automatically have also a superconducting state.

BCS theory is a microscopic theory which explains why these Cooper pairs are formed. They are fromed, because the interaction between the electrons and the phonons causes an effective and attractive interaction between the electrons. Once you have an attractive interaction between the electrons the Cooper pairs are almost bound to form.

You can guess in what way the unconventional superconductors step out: in this case the Cooper pairs are still formed, but the mechanism that causes it is fundamentally different from ordinary BCS. BCS theory is definitely correct - it's just not applicable to the unconventional ones.

4. Jul 26, 2009

### ZapperZ

Staff Emeritus
Er.. I think a few things need to be clarified here a bit.

The BCS theory, while it was originally based on electron-phonon coupling as the mechanism for the formation of Cooper Pairs, is actually quite independent of this. It just happened that when BCS theory was formulated, this mechanism is the only one known for Cooper Pair formation. But if you look at the theory itself, one can use almost any kind of mechanism for the pairing. It is why, even for high-Tc superconductors, there have been attempts to introduce the magnetic, or spin fluctuation, within the BCS theory as the mechanism for coupling. So essentially, BCS theory works for almost any kind of electron-bosonic coupling.

Now, having said that, I think what the OP has been told can be interpreted in 2 different ways from my perspective:

1. The "electron-phonon" coupling is being attached to BCS theory and thought to be the same thing. So when high-Tc superconductors were discovered that cannot be explained by conventional electron-phonon coupling, this was then concluded that this is non-BCS.

2. The non-conventional properties of high-Tc superconductors that have characteristics of non-Fermi liquid normal state and non-BCS behavior.

Without having a clearer picture of what is being described, it is difficult to know which of the two was being used.

There are many indications that, at least for the cuprate superconductors, that BCS theory may not hold. This is certainly true if one buys into either the Stripe model, or Anderson's RVB model. Still, until those are sorted out one way or the other, many of the properties of these superconductors are still derived using parameters that are clearly defined within the BCS theory and the Fermi liquid theory themselves. ARPES measurement of the single-particle spectral function have self-energy terms that are defined as part of the Fermi liquid theory, for example. These are the values that we continue to extract out of these experiments.

Zz.

5. Jul 27, 2009

### Mentallic

So basically there are two theories that are used to explain two different mechanisms for creating a SC. I would like to understand why electron-coupling doesn't apply for high Tc SC's and vice versa, but I know this will lead me into a deep dark road on this subject, which I would have to learn from scratch.
Can I instead ask, why is it a goal for scientists to somehow combine the theory of relativity with quantum mechanics to unite the forces when it could so happen that they can only be explained by two theories - similarly to the SC theories?

6. Jul 27, 2009

### ZapperZ

Staff Emeritus
Er... electron-coupling to a bosonic mode IS the dominant theory right now for ALL superconductivity. So I'm not sure where this "doesn't apply to high-Tc superconductors". It just that this bosonic mode may not be phonons (or it might still be the half-breathing optical phonon mode if the phonon crowd is correct).

This is now a separate question rather unrelated to your original topic. I don't believe you want to hijack your own thread.

Zz.

7. Jul 27, 2009

### Mentallic

If so, I guess I have failed to understand why the mechanisms are different while the electron-coupling involves both types of SC's.

But this is where I was planning to head towards incase my skepticism was denied, in which case it has been. I want to understand why these two theories both apply independently (for what I believe to be two sides to the same coin) when such other examples of multiple theories that seemingly clash isn't acceptable - in this case, relativity + quantum mechanics.

p.s. Is it an offense to hijack my own thread?

8. Jul 27, 2009

### ZapperZ

Staff Emeritus
What "two theories" are you talking about?

I've already stated that BCS is STILL being used, even for the high-Tc superconductivity, especially in extracting many of the characteristics that we get from measurements! So what are these 'two theories'? Having different bosonic coupling does NOT change the theory. It changes the source of the coupling, but the description of the interaction remains the same! Do you have different theories if your "F" in "F=ma" is due to electromagnetic origin versus gravitational origin?

This is getting to be highly confusing. Special Relativity doesn't "clash" with quantum mechanics. It's been incorporated quite well, thank you! So what are we talking about here.

And yes, it is against the rule to hijack even your own thread. It creates a confusing and meandering thread. Create another thread if you wish to change the subject of the discussion.

Zz.

9. Jul 27, 2009

### maverick_starstrider

You're comparing apples and oranges. The perceived problem with having general relativity and quantum as seperate are that those are separate frameworks that describe how the same universe exists and they don't agree on certain things. Which means that both can't be right, plus even if they didn't disagree it would seem inconceivable to most people that at some random absolute length/size scale that quantum theory simply "turned-off" and GR "turned-on".

Whether or not BCS theory accounts for the superconducting phase in unconventional superconductors really has absolutely nothing to do with in content or spirit, GUT. Think about cooking something. You put it near something really hot, like an over or a fire, and it gets cooked. Therefore you develop a theory of cooking that involves how to cook by placing these next to hot objects. However, then someone comes along and invents the microwave and now you realize that things can be cooked without putting them next to a hot object.

In this example a certain state (being cooked) can be achieved multiple ways. Did the discovery of the microwave negate the effectiveness of placing next to hot objects? Did it have anything to do with disproving it? No. And ultimately microwaves cook in a different way then fire (from the inside, and they work better on things with lots of water on them, etc.)

This is what we have with superconductivity. The existance of unconventional superconductor in no way undermines the correctness of our theoretical understanding of the formation of superconducting states in conventional superconductors (no more then the invention of the microwave casts doubt on the theory that when you place something near a hot object it will get cooked). We simply discovered that there may be more than one way to skin a cat. It maybe possible to reach a superconducting state that doesn't originate from the phenomena described in BCS.

10. Jul 29, 2009

### genneth

ZapperZ: do you have any links to good reviews of the phonon line of thinking? I've been a little biased towards the magnetic side due to my, err, upbringing

11. Jul 29, 2009

### ZapperZ

Staff Emeritus
My academic career was also "colored" with the magnetic fluctuation picture, so I'm leaning more towards it.

Since I pay more closer attention to the ARPES experiments, I can point to you the most significant paper from such experiment that argued for the phonon picture. It addresses what is commonly called the "kink" in the ARPES dispersion in high-Tc superconductors. While several group (including the one that I used to work in) argued for the magnetic origin of this kink, the group from Stanford[1] argued for this kink to be the signature of a coupling to a phonon mode. Since then, the half-breathing phonon mode by the apical oxygen in the lattice has been identified as having that characteristics.

Zz.

[1] A. Lanzara et al., Nature v.412, p.510 (2001).

12. Jul 29, 2009

### kanato

Can BCS predict non s-wave symmetry in the gap function?

13. Jul 29, 2009

### genneth

Thanks for the link, it's a useful start to trying to piece together the work on this approach. However, I'm an avowed theorist, so what I would really like to see is a good summary of the main features described by the theory, and also a criticism of the features apparently missing. Sometimes it seems like certain issues are being completely ignored, but it's not clear whether it's because it's too hard or because everyone (but me) already knows the answer.

For instance, I'd like to know the explanation that the various camps have for things like the asymmetric tunneling, or the anomalous transport properties --- I'll happily accept "don't know" as a valid answer.

For instance, as far as this kink goes, I can imagine the RVB camp's defense to go something along: we always said that optical phonons will couple, probably strongly --- it's an oxide after all; but the coupling can't be the origin of the superconductivity, because:

1. d-wave requires space avoidance; phonons give time avoidance

2. any attempt to reach SC via a Fermi liquid (in the sense of the renormalisation running as Strongly interacting system -> Fermi liquid -> SC) will have a symmetric tunneling spectum

3. etc. (I'm not Anderson )

I'd also like to see arrguments to where the RVB approach clearly ignores some (critical) feature...

14. Jul 29, 2009

### ZapperZ

Staff Emeritus
That has nothing to do with BCS directly. It is due to the "glue". If you look at the early tunneling data and analysis (say mid 1990's to early 2000), there have been many analysis of tunneling spectra that used BCS/Mean Field approach but with d-wave gap symmetry.

What you should ask if phonon coupling can produce non s-wave symmetry, or in particular, the $d_{x^2 - y^2}$ symmetry.

Zz.

15. Jul 29, 2009

### ZapperZ

Staff Emeritus
There was either a paper, or a preprint, by Phillip Phillips, addressing the theoretical viability of phonon coupling for HTS. I'll look it up when I'm back in the office if you haven't found it before then.

Zz.

16. Jul 29, 2009

### ZapperZ

Staff Emeritus
I stand correct. It wasn't Phillip Phillips of UIUC, but rather JC Phillips at Bell Labs. The reference is Philosophical Magazine Part B, 82:8, 931 (2002).

Zz.

17. Jul 29, 2009

### genneth

Thanks again for the link. :-) I've skimmed it, and it's interesting to see what experimental features are focused on; however, unless I'm mistaken, the paper completely ignores the fact that the cuprates exhibit d-wave symmetry?

18. Jul 30, 2009

### Minich

Exclusive and excellent question!!!
But i guess, you don't get the answer in this thread :(

"Two electrons" and only TWO(!!!) may attract each other with the glue (phonons, exitons, magnons, spinons,...) -------->>>

"Two attracted electrons" form quasiboson: so-called Cooper pair ----->

Gas of Cooper pairs is almost "IDEAL" Bose gas ----->

At some temperature Cooper pair bose gas becomes BEC condensed ----->

BEC condensed Cooper pair bose gas MUST(!!!???) BE superconducting ---->

Thats all You can get in this thread!!!

So unified theory of superconductivity for conventional and unconventional SC already exists:

(Two electrons)+glue+BEC

)

19. Jul 30, 2009

### ZapperZ

Staff Emeritus
This is patently false, and I strongly suggest that you CEASE this repeated line of fallacy immediately.

I already mentioned Anderson's RVB model which lacks any kind of paring mechanism! So to accuse this thread of ignoring such a possibility is clearly wrong. You think there's a better mechanism? PUBLISH IT!

Zz.

20. Jul 30, 2009

### Minich

To ZapperZ.
I also know Frohlich theory of SC without paring of 1954 yo, but where is it now?
There are more than 20 theories of HTSC shurely WITH Cooper paring and BEC.
How many theories of HTSC do you know WITHOUT Cooper paring and BEC, except RVB?
I'll be very pleased for getting references.

Sincerely yours, Minich.