Don,

Well, a rather simplistic model might say that since the electrons are not localized in the superconductor, the material *cannot* support a thermal gradient.

(hey, it works for me!)

Edit: Not the full story, not even true. See below.

James,

So are your saying that the temperature gradient causes displacement of the electrons in  the metal thus producing electron localization and that this doesn't occur in the superconductor, If so then how do the electrons, in this case the copper pair electrons, behave in a superconductor subjected to a temperature gradient?

Don,

Apologies, I wasn't clear. Since the electrons face no barrier to movement (there are no forces that localize them) throughout the superconductor, a gradient cannot be supported - any attempt to locally raise their temperature simply spreads that heat over the bulk material.

Edit: Not true. The formation of Cooper pairs (a la BCS...) reduces the availability of electrons to transport heat. Thermal conductivity will fall with falling temperature.

James,

So in essence you are saying that where ever the heat is applied to a superconductor it will instantaneously be spread through out the superconductor?

Don,

I'm going to retract everything that I thought I knew about superconductivity.

Please disregard my earlier comments.

I was utterly wrong.

Briefly, when sufficiently cold, in the BCS theory electrons pair up to form boson-like objects. They are no longer able to act as carriers of heat.

So the contribution to thermal conductivity from electrons becomes weaker. And this 'normal' thermal conductivity falls as the temperature also falls.

As more electrons pair up, the ability to move heat lessens and in all examples that I've seen so far, the thermal conductivity tends to zero at 0K.

(albeit with some interesting material-specific maxima along the way that might be ascribed to the ever-scarcer phonon-electron scattering)

I'll edit my posts to show my error. Thanks! I've learned stuff today!

I'm looking at Wesche, 'Physical Properties of High-Temperature Superconductors'

James,

Thanks for the clarificaion. In Wesche's 'Physical Properties of High-Temperature

Superconductors' the subject is High-Temperature Superconductors so this book

must be primarly about ceramic not metal superconductors. But now as you said

earlier when sufficiently cold, in the BCS theory electrons pair up to form

boson-like objects. They are no longer able to act as carriers of heat. So the

contribution to thermal conductivity from electrons becomes weaker. And

this 'normal' thermal conductivity falls as the temperature also falls. Does this

mean that even in an isolated superconductor metal strip that is cooled at one

end and heated at the other end that BCS electron paring is taking place? If

this is true than electrons may not need to be moving for BCS paring to take

place and it could be that the passage of phonon energy waves bring about

BCS paring!

 P.S.

I found in an article from the University Maryland titled High temperature

superconductivity reveals its secret that the BCS standard electron-phonon

mechanism cannot explain the ceramic Cooper pairing found in the high-

temperature superconducting (high-Tc) cuprates. It appears to be a modified

version of BCS paring.

James,

According to J.R. Waldrams book Superconductivity of Metals and Cuprates Thermoelectric effects.

  In an isolated normal metal, heated at one end and cooled at the other, the thermoelectric forces generate a cancelling thermal gradient but no current flows, but a superconductor, under similar conditions, generates a continuous normal thermocurrent which is cancelled out by a back flow of supercurrent and there is no thermal gradient.

In a normal metal thermocouple loop circuit there is a net EMF and a thermocurrent circulates, with emission or absorption of Thompson heat from the wires and emission or absorption of Peltier heat from the junctions. In a superconducting thermocouple loop circuit the thermocurrent is cancelled out by the supercurrent backflow. If current is forced to circulate in a normal metal thermocouple loop circuit there is Thompson or Peltier heating but not in a metal superconductor thermocouple loop circuit.

There is no net current in the bulk of the superconductor thermocouple loop circuit but the presence of the supercurrent backflow can be detected because the trapped flux (phi) changes and a corresponding small screening current flows on the inside surface of the circuit loop. 

Don,

You are correct, Cooper pairs are a viable explanation for superconductivity in metals, but high Tc materials appear to be less well-understood.

Thank you for raising this question, and in turn allowing me to unlearn my prejudices!

James,

Here is a correction to an entry earlier.

Does this mean that even in an isolated superconductor metal strip that is cooled at one end and heated at the other that BCS electron paring is taking place?

If this is true than electrons may not need to be moving for BCS paring to take

place and it could be that the passage of phonon energy waves bring about

BCS paring!

 This turns out not to be true according to the following information,,,

 Electrons in a Cooper pair have opposite spins – hence Cooper pair has zero spin i.e. acts as a boson

Bosons do not obey exclusion principle  ®  can all occupy same quantum state of same energy

Consequences: Cooper pairs act in a correlated way via phonon energy waves. So, in this collective state, they can all move together.

Binding energy of Cooper pair is largest when all are in same state. A cooperative phenomenon.

Don,

It's stranger than that - my understanding is that Cooper paired electrons have opposite momenta *and* opposite spin.

http://physics.stackexchange.com/questions/111621/why-are-cooper-pairs-formed-by-electrons-of-opposite-momentum-and-spin

I'm reminded of Haldane's quote.

James,

 Indeed: My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose.

  A rube goldberg sort of universe

Hi Remi,

   Thanks for contributing to this discussion,

   I, for the most part, agree with what you have written. The following is a minor modification to what you wrote.

   At different temperatures, this Fermi level will shift upwards as electrons occupy higher energy levels. The tendency of electrons is to diffuse not flow from regions of high (temp.) energy to lower (temp.) energy in a single metal, the Seebeck effect.  But there is electron flow from high concentration to low electron concentration between two metals in contact. This chemical potential occurs between two metals not in a single metal. Now, in a single metal, as the electron concentration gradually builds up at the cold end and is lowered at the hot end of the single metal in question, Seebeck effect, this effect also gradually produces a counter EMF that gradually will resist the further accumulation of electrons for a set temperature difference. This effect is similar to what happens as an electronic capacitor gradually builds up in charge and as it does so there is also a gradual counter EMF that acts to resist further electron increase until equilibrium is reached according to what the set voltage is.

 According to J.R. Waldrums book titled Superconductivity of Metals and Cuprates,

   In a superconductor something different happens. We cannot set up a gradient of electron mobility (chemical potential) µ, and the thermoelectric forces therefore drive a continuous normal thermocurrent along the metal sample. We may use the analysis of Section 2.5 in this situation, identifying Jres as the normal thermoelectric current Jth. Since in a uniform material Jth is proportional to ∇ T we know that ∇ ^ Jres = 0 in (2.13), so the magnetic screening equation (2.14) holds in the usual way, in spite of the presence of the normal thermocurrent. It follows that the total current density must be zero deep inside the superconductor, as usual: the supercurrent must therefore exactly cancel the normal thermocurrent in the *(Fig. 2.8b). Because the Seebeck EMF acting on the normal electrons is always short-circuited by the supercurrent, a superconductor placed in a thermoelectric circuit contributes nothing to the circuit EMF. The absence of any contribution by a superconductor to the circuit Seebeck EMF is in fact very useful: It makes it possible to measure the thermopower of a single metal in isolation, by measuring the total EMF of a thermocouple made up of the normal metal in question and a superconductor.

* Could this exact cancellation of the normal thermocurrent be due to the more fundamental effect of Lenz’s Law?

 Remi,

Why is this wrong, please explain,

 This difference in chemical potential occurs between two metals not in a single metal. "

Remi,

You said that the statement  "This difference in chemical potential occurs between two metals not in a single metal. " is wrong without some sort of explanation.

 Remi, I would expect that if someone makes a statement such as this or that is wrong  they provide, out of respect , some information that supports their view. So once again

Why is this wrong, please explain,

It's all well and good to say that  There can be a difference in chemical potential in one piece of metal. But be reasonable and provide an example or reference that supports your statement!

   After looking further into the matter per your ref. info. It looks like the term chemical potential may be appropriate even in the case of an isolated metal sample, whose ends have a temperature difference, due to different Fermi energies. Now in the second part of my initial email, concerning J.R. Waldrums book titled Superconductivity of Metals and Cuprates,  In your previous email you said thus there is no difference in chemical potential to drive the thermoelectric effect in a superconductor.  Sounds like you are implying that the thermoelectric effect does not exist in an isolated superconductor.  But in J.R. Waldrums book, it states that in a superconductor something different happens. We cannot set up a gradient of electron mobility (chemical potential) µ, and the thermoelectric forces therefore drive a continuous normal thermocurrent along the superconductor metal sample. Can you provide some information to clear up this point which was the reason I initially raised the question Why does an isolated normal metal when compared to a superconductor exhibit very different thermoelectric effects?

Remi,

You haven't responded to my last email. I provided you the the title of J.R. Waldrums book that contains the statement. "We cannot set up a gradient of electron mobility (chemical potential) µ, and the thermoelectric forces therefore drive a continuous normal thermocurrent along the superconductor metal sample." This appears to contradict your statement  that "there is no difference in chemical potential to drive the thermoelectric effect in a superconductor". Now if you have an issue with what J.R. Waldrums is saying and that is why you haven't responded then say so and not respond like a child that runs away because they don't want to play anymore !!!