# Thermal Superconductor

#### ChmDudeCB

Go easy on me, as I have no formal condensed matter education and just the highest undergraduate quantum physics and chemistry offered at my university. I read a lot of papers and did extra studying while taking those classes, but I'm definitely rusty on the mathematics. Feel free to give me juicy stuff, though, because I have a couple quantum books whose mathematics reference appendices have never failed me and I can always come back later and figure it out.

Would it be at all possible to design a thermal superconductor? That is, the vibrational excitations of the particles is transferred at c, or even more weird, instantly. Also, given the relationship between thermal conductance and electrical conductance above superconducting temperatures, would there be a relation? Am I asking a question that is already well known? :yuck:

Last edited:
Related Atomic and Condensed Matter News on Phys.org

#### ZapperZ

Staff Emeritus
2018 Award
Go easy on me, as I have no formal condensed matter education and just the highest undergraduate quantum physics and chemistry offered at my university. I read a lot of papers and did extra studying while taking those classes, but I'm definitely rusty on the mathematics. Feel free to give me juicy stuff, though, because I have a couple quantum books whose mathematics reference appendix have never failed me and I can always come back later and figure it out.

Would it be at all possible to design a thermal superconductor. That is, the vibrational excitations of the particles is transferred at c, or even more weird, instantly. Also, given the relationship between thermal conductance and electrical conductance above superconducting temperatures, would there be a relation? Am I asking a question that is already well known? :yuck:
Er... you failed to completely explain what kind of a mechanism that will form the supercurrent with this "thermal conductor".

We already know that the "vibrational modes" (phonons) of the lattice provides the "glue" in the pair formation for conventional superconductors. I'm not sure if this is what you are referring to, but I doubt it because these are not "transferred at c" by any means. But thermal fluctuations are the enemies of pairing formation and long-range coherence. So I fail to understand what you mean by "thermal superconductor".

The relationship between thermal and electrical conductance in an ordinary conductor is related to the Wiedermann-Franz law.

Zz.

#### ChmDudeCB

What I mean by a thermal superconductor is that if you have an addition of thermal kinetic energy to one end of a continuous piece of the material the rate of heat transfer would nearly instantaneous. If uniform temperature is necessary for pairing then I doubt this is at all probable.

#### ChmDudeCB

Also, does this mean that thermal fluctuations hamper electrical superconductance causing discontinuities in conduction as a function of distance?

#### ZapperZ

Staff Emeritus
2018 Award
What I mean by a thermal superconductor is that if you have an addition of thermal kinetic energy to one end of a continuous piece of the material the rate of heat transfer would nearly instantaneous. If uniform temperature is necessary for pairing then I doubt this is at all probable.
Also, does this mean that thermal fluctuations hamper electrical superconductance causing discontinuities in conduction as a function of distance?
Er.. I'm not sure what I'm missing here.

Think about it. If you heat up a superconductor (i.e. increasing the thermal fluctuation), it becomes normal conductor. This is a clear evidence that heat destroys superconductivity.

So your proposal of ADDING heat to a superconductor to induce superconductivity is puzzling. You did not describe the mechanism to form the supercurrent. There certainly is nothing that we know and have verified to justify such a scenario.

P.S. heat does NOT get transfered "nearly instantaneously". Where did you get that idea?

Zz.

#### Antiphon

The best you could hope for is sub-c thermal propagation.

The correct analogy to a superconductor is that it has a uniform temperature everywhere no matter where or how it was heated.

#### ChmDudeCB

The best you could hope for is sub-c thermal propagation.

The correct analogy to a superconductor is that it has a uniform temperature everywhere no matter where or how it was heated.
Precisely.

I'm not suggesting we add heat to promote superconductance, it is my understanding that a material exhibits superconductance below a certain temperature. For instance, lets say substance X reaches superconductivity at 40K. If it is at 20K and I gently add heat (as to not raise any portion above 40K) does the temperature rise in a uniform fashion throughout the material and if not does the temperature differential cause discontinuity in the electrical superconductance?

#### ZapperZ

Staff Emeritus
2018 Award
Precisely.

I'm not suggesting we add heat to promote superconductance, it is my understanding that a material exhibits superconductance below a certain temperature. For instance, lets say substance X reaches superconductivity at 40K. If it is at 20K and I gently add heat (as to not raise any portion above 40K) does the temperature rise in a uniform fashion throughout the material and if not does the temperature differential cause discontinuity in the electrical superconductance?
Er... why would it rise any differently in the superconducting state versus non-superconducting state. The electron gas does not have that high of a specific heat capacity when compared with the lattice ions. In other words, if you have the same material at 20K, and you put it in a high enough magnetic field that it is above critical and in the normal state, the heat conductivity for both material (one in superconducting state, the other in the normal state) being heated at one end should be practically the same!

Zz.

#### ChmDudeCB

Hmmmm.

I thought electron gas was an idea left behind in the 1800's.

Electrical superconductance is essentially zero resistance/impedance. In the realm of classical materials, electrical conductance is directly proportional to thermal conductance. Due to the idea/theory of the phonon, the perfect electrical conductance is due to the wave functions of every particle being interdependent upon the entire wave function of the system. Thus, my idea is that a kinetic increase would share a similar property.

#### ZapperZ

Staff Emeritus
2018 Award
Hmmmm.

I thought electron gas was an idea left behind in the 1800's.

Electrical superconductance is essentially zero resistance/impedance. In the realm of classical materials, electrical conductance is directly proportional to thermal conductance. Due to the idea/theory of the phonon, the perfect electrical conductance is due to the wave functions of every particle being interdependent upon the entire wave function of the system. Thus, my idea is that a kinetic increase would share a similar property.
You seem to not have realized about the importance of the formation of Cooper pairs, and then the condensation into the superconducting state. May I suggest you start with the BCS theory first?

Zz.

#### ChmDudeCB

I'll hit the 'brary this week if I have time. I'm headed back to the Uni for my last undergrad semester today.

Maybe you want to read about super fluid helium and second sound. There is no light speed propagation of heat, but very fast propagation. When materials become superconducting their thermal conductivity decreases, because the cooper pairs do not interact with the phonons anymore, and the electronic conduction of heat stops. So it might be unintuitive but super conductors are poor thermal conductors, this is well known and there are temperature valves realized by enabling and disabling superconductivity with magnetic fields.

#### Pluthos

I am intrigued by this question and I don't have an answer. Here is a thought experiment. A superconducting rod is terminated at each of its ends with a non-superconducting material (for example the material could be different at each end or a magnetic field could be present at each end). If a temperature difference exists between the two ends keeping the temperature at each end below the critical temperature, how is the heat transmitted from one end to the other? Is it only by lattice phonons? Do cooper pairs contribute to the heat conductivity? How good are they at transmitting the heat?

#### M Quack

There are two main contributions to thermal transport in solids:

Electrons and Phonons (lattice vibrations)

Superconductivity essentially switches off the electronic heat transport. Cooper pairs do not contribute to the thermal conductivity. So this leaves only the phonon transport.

Phonon heat transport has a very strong temperature dependence. At low (superconducting) temperatures it is very low.

Therefore a low-temperature superconductor has extremely low thermal conductivity in the superconducting state. Was was pointed out above, you can "switch back on" the electronic transport by destroying superconductivity with a magnetic field.

The phonon part depends on the dispersion curve of the phonons. To cut a long story short, hard materials are better (phonon) thermal conductors. Diamond is extremely hard, and it is one of the best non-metalic thermal conductors.

The electronic part depends on the electrical conductivity. Better electrical conductors are better thermal conductors (as long as you stay away from superconductivity). Copper, Silver, and Aluminium are all good electrical and good thermal conductors. Stainless steel is a poor electrical and thermal conductor.

Interestingly, holes can transport heat just as well as electrons (for example in semiconductors).

#### ImaLooser

Astrophysicists believe that the cores of neutron stars are both superconducting and superfluid at 500,000,000 K and less. The speed of sound in such a fluid is one half the speed of light, and the speed of thermal conduction about the same I would guess.

#### ZapperZ

Staff Emeritus
2018 Award
The question that has been posted is a bit vague. Are we looking only at the interface between the superconductor and the normal metal?

The physics involved here isn't that trivial, so I'm not sure to what level of sophistication we want to deal with. For example, it is well-known that the proximity effect can be established at such an interface. Naively, the wavefunction of the Cooper Pairs "leaks" out to some extent into the normal metal.

On the other hand, the Cooper pairs, very much like the electron gas in metals, do not have a high specific heat. So to what extent would they be involved in heat transport? So one can already see that this can be a tricky thing to answer, depending on how much detail one wants to deal with.

Zz.

#### DrDu

Interesting question. I think 0xDEADBEEF answer is nearest to the question. Superfluid He in deed conducts heat several orders of magnitude better than does normal liquid He.

#### Pluthos

MQuack, you are saying:
"Superconductivity essentially switches off the electronic heat transport. Cooper pairs do not contribute to the thermal conductivity."
I supposed this is true because the Cooper pairs are completely decoupled from the lattice. This is precisely why they are superconducting. This is only true in the bulk of the superconductor. At the edges where the superconductor makes contact with non-superconductor material this is no longer true and electrons do interact with the lattice. Electrons also associate into and out of Cooper pairs. So the question remains: is it possible for heat to go from one side of the superconductor to the other by means of the Cooper pairs? and if so would this heat be quasi-instantaneoudly tranmitted?

#### ZapperZ

Staff Emeritus
2018 Award
MQuack, you are saying:
"Superconductivity essentially switches off the electronic heat transport. Cooper pairs do not contribute to the thermal conductivity."
I supposed this is true because the Cooper pairs are completely decoupled from the lattice. This is precisely why they are superconducting. This is only true in the bulk of the superconductor. At the edges where the superconductor makes contact with non-superconductor material this is no longer true and electrons do interact with the lattice. Electrons also associate into and out of Cooper pairs. So the question remains: is it possible for heat to go from one side of the superconductor to the other by means of the Cooper pairs? and if so would this heat be quasi-instantaneoudly tranmitted?
Er... heat transport and current transport are not the same thing. That's why you have DIFFERENT coefficients of thermal transport and electrical transport! In fact, in 1D metals, the Wiedemann-Franz Law has been shown to be violated.

So there's nothing here that would indicate that heat is "quasi-instantaneously" transmitted. If it is, those people cooling the superconducting magnets, especially at the LHC, won't have issues with heat transfer... but yet, they do!

Zz.

#### M Quack

Superconducting thermal switches are used in many ultra-low temperature experiments such as (nuclear) adiabatic demagnetization. They are _very_ efficient.

What you are asking is: Can a Cooper pair be broken at the hot side, taking up energy, travel to the cold side and recombine, giving off energy and thus heating the cold side.

Off the top of my head I can think of two arguments why this effect should be small in SC:

1. it will be limited by the free path length of the (normal conducting) electron
2. To break the Cooper pair you need an energy larger than the SC gap. At SC temperature the statistical occurrence of such fluctuations is small (otherwise the material would not be in the SC state).

Assume you do break a Cooper pair, and the hot electrons travel a small distance into the SC. They will recombine somewhere slightly colder, where the chances of breaking a new pair to transfer the heat further are even smaller than at the starting point. So the heat transfer mechanism will die out very quickly as you go deeper into the cold SC.

#### chill_factor

the question has been misunderstood i think, this is my interpretation.

There is a thermal analog of electrical conductivity: thermal conductivity.

Is there a thermal analog of electrical superconductors, that is, something that conducts thermal energy with no resistance (that is, the specimen will have the same temperature at all points within the time it takes light to travel from 1 end to the other in all cases)?

#### Per Oni

On the other hand, the Cooper pairs, very much like the electron gas in metals, do not have a high specific heat. So to what extent would they be involved in heat transport?
Zz.
Sometimes I wonder whether electrons are involved in thermal transport at all. The reason I say this is because at very low temperatures, typically from T close to zero K up to T around 15 or 20 K, we have a low thermal conductivity in all metals but a high electrical conduction. This behaviour would make sense to me if thermal conductivity is caused only by phonons.

#### Pluthos

Just a conjecture. We may have some kind of reverse Mossbauer effect. Phonons which are below the energy of the lattice are either reflected or transmitted quasi-instantaneoulsy to the other side of the material

#### M Quack

Just a conjecture. We may have some kind of reverse Mossbauer effect. Phonons which are below the energy of the lattice are either reflected or transmitted quasi-instantaneoulsy to the other side of the material
For that you have to get rid of acoustic phonons which always go to zero energy at the Gamma point.

#### zhanhai

I am intrigued by this question and I don't have an answer. Here is a thought experiment. A superconducting rod is terminated at each of its ends with a non-superconducting material (for example the material could be different at each end or a magnetic field could be present at each end). If a temperature difference exists between the two ends keeping the temperature at each end below the critical temperature, how is the heat transmitted from one end to the other? Is it only by lattice phonons? Do cooper pairs contribute to the heat conductivity? How good are they at transmitting the heat?
I doubt whether it is possible to establish a temperature difference between two ends of a single crystal without destroying it. Even if a bulk of material is a single crystal, it might be impossible to establish a temperature difference across it without destroying its original lattice.

Phonon is only associated with its (single) crystal lattice. It is the quantum of interaction with the lattice AS A WHOLE.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving