What is the Isotope Effect and its Role in Superconductors?

[johnnyb20023]

I am doing a report on superconductors. One of the ideas to support the idea of bandgaps in the superconductor is the isotope effect. Unfortentualy I have been an able to find any information on how exactly the isotope effect works. Any information would be greatly appreciated, thank you

 

[ZapperZ]

I am doing a report on superconductors. One of the ideas to support the idea of bandgaps in the superconductor is the isotope effect. Unfortentualy I have been an able to find any information on how exactly the isotope effect works. Any information would be greatly appreciated, thank you

I think you may be confused about something. The "idea of bandgaps" in a superconductor isn't really supported by the isotope effect. However, the SIZE of the gap may be correlated with the isotope effect. The isotope effect in conventional superconductor was one of the key evidence pointing towards phonons as the pairing mechanism.

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/coop.html#c5

Zz.

 

[johnnyb20023]

Reply to ZapperZ

Yes I saw that on hyperphysics yet it does not explain the workings of the isotope effect basically says "hey look this works so there". What I was looking for was an explnation of the isotope effect. Thank you though for your input. Still

 

[ZapperZ]

Yes I saw that on hyperphysics yet it does not explain the workings of the isotope effect basically says "hey look this works so there". What I was looking for was an explnation of the isotope effect. Thank you though for your input. Still

Think of a spring. The natural frequency of oscillation corresponds to the inverse of the square root of the mass. This means that the larger the mass, the smaller the frequency. Consequently, the normal mode phonon frequency (or energy) becomes becomes smaller. This translates directly to the coupling strength that these phonons can interact with the electrons to form the cooper pair. The smaller the energy, the smaller the coupling strength, the lower the Tc. Thus, with everything else being the same, the larger mass or isotope of the same element will tend to show a lower Tc.

This is why the isotope effect is a clear signature of phonons playing the major role in the superconducting mechanism... at least for the conventional superconductors.

Zz.

 

[johnnyb20023]

Thank You

Thank you that helped to answer my question.

 

[Creator]

This is why the isotope effect is a clear signature of phonons playing the major role in the superconducting mechanism... at least for the conventional superconductors.

Zz.

Good explanation Zapper. Why doesn't it 'work' for HTS?

Secondly, doesn't it seems rather strange that the pairing mechanism could only arise from lattice interaction (in conventional superconductors) whereas in every other example of fermion pairing condensates there appears to be no such requirement?
Creator

 

[ZapperZ]

Good explanation Zapper. Why doesn't it 'work' for HTS?

Secondly, doesn't it seems rather strange that the pairing mechanism could only arise from lattice interaction (in conventional superconductors) whereas in every other example of fermion pairing condensates there appears to be no such requirement?
Creator

There is nothing special about phonons being the pairing mechanism. It just happens that they are in abundance in the most common material that undergoes such pairing/condensation. In fact, if you look at the BCS paper itself, the theory is independent of phonons as the mediator of the pair. It just happened that they used phonons as an example. You could substitute phonons with any bosonic mechanism in that theory and it will still work. In He3, BCS theory works pretty well even when the pairing is due to dipole-dipole interaction.

The high-Tc superconductors are of a different beast entirely. The material started off as an antiferromagnetic INSULATOR. This is already different than the conventional superconductor that begin life as a normal conductor. It is only when you sufficiently dope the insulator (by increasing the number of electrons or holes) that it will eventually become a superconductor. Furthermore, the "insulator" isn't your typical band insulator. It is a Mott insulator in which the reason charges can't move is not because there are no empty states to occupy, but because there are long range antiferromagnetic ordering. A charge carrier of the "wrong" spin simply can't jump to the next site. So all the charge carriers in the material are "strongly correlated" - they "sense" each other too strongly and can't simply go where ever they like.

It is because of these strong spin correlation that spin fluctuation/magnon is one of the leading contender of the pairing mechanism for these material. I will qualify my prejudice in stating that since I have published papers advocating that point based on the ARPES measurements that I have performed. But there are certainly other groups advocating other mechanisms, even phonons (Stanford's group of Z.X. Shen). This issue here is certainly far from being resolved.

Zz.

 

[Creator]

"In fact, if you look at the BCS paper itself, the theory is independent of phonons as the mediator of the pair. It just happened that they used phonons as an example. You could substitute phonons with any bosonic mechanism in that theory and it will still work.."

Thanks for clarifying that; most of these articles seem to make one think phonon mediation is necessary for BCS and use isotope effect as a unique justification. My opinion is that the isotope effect may not be unique to phonon interaction, other underlying mass dependent correlations may be possible.

"It is because of these strong spin correlation that spin fluctuation/magnon is one of the leading contender of the pairing mechanism for these material."

Since you appear to be very knowledgeable in this area (spin fluctuation is my area of weakest understanding) please give a simple explanation of spin fluctuation and how it can account for the pairing state.

And secondly, please explain how angular resolved photo emission is used to validate that mechanism.

 

[ZapperZ]

"In fact, if you look at the BCS paper itself, the theory is independent of phonons as the mediator of the pair. It just happened that they used phonons as an example. You could substitute phonons with any bosonic mechanism in that theory and it will still work.."

Thanks for clarifying that; most of these articles seem to make one think phonon mediation is necessary for BCS and use isotope effect as a unique justification. My opinion is that the isotope effect may not be unique to phonon interaction, other underlying mass dependent correlations may be possible.

"It is because of these strong spin correlation that spin fluctuation/magnon is one of the leading contender of the pairing mechanism for these material."

Since you appear to be very knowledgeable in this area (spin fluctuation is my area of weakest understanding) please give a simple explanation of spin fluctuation and how it can account for the pairing state.

And secondly, please explain how angular resolved photo emission is used to validate that mechanism.

The isotope effect is a very strong signature for phonon mechanism. But in conventional superconductor, it isn't the only clue that phonons are the "culprit". Tunneling measurements also show very convincing evidence for this. Now whether the isotope effect can also imply other forms mechanism, or may be due to other "red herrings", that I do not know.

Spin fluctuation is, to put it crudely, is the exchange of spinons as the mediator for paring. Since the "background" of the material is highly spin oriented, it is natural to think that these things play a role in the paring, at least from my point of view. This is very much similar to the background of phonon fields that electrons in conventional superconductors see.

As for ARPES, I can offer you a couple of very good review articles on its application in the study of high-Tc superconductors:

http://arxiv.org/abs/cond-mat/0209476
http://arxiv.org/abs/cond-mat/0208504

These were written by very well-known experts in this field.

Zz.