# Why do superconductors superconduct current?

## Main Question or Discussion Point

Hello,

which theory or formalism is used to show the superconductors have zero resistance? I'd like to see some derivation from microscopic principles.

For resistivity scattering is crucial so a static wavefunction doesn't offer an explanation?

I read some basic BCS theory and have vaguely heard about Green's functions. What should I read (book?) to see why there is no resistance.

I think the only way to understand physics is to follow the exact mathematical derivation, because I want to understand the phenomenon and not just "justify" it.

Anton

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I found an old copy of this book. There it mentions the usual stuff about thermodynamics and magnetic behaviour, but I couldn't spot a treatment of electrical conductivity?!

f95toli
Gold Member
Tinkham's "Introduction to Superconductivity" covers the electrodynamics in some detail.
However, if you really want a rigorous treatment you need to a book on solid-state many-particle physics since this requires some rather sophisticated techniques (e.g. Nambu-Gor'kov formalism). I have a copy of Zagoskin's "Quantum theory of Many-body systems" and that covers among other things the current-carrying state.

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because its diamagnetic

malawi_glenn
Homework Helper
because its diamagnetic

There are diamagnets that are not SC, so that is not the case. However perfect diamagnetism arises due to SC.

i meant perfectly diamagnetic

i meant perfectly diamagnetic
That is not related to my question. I asked why the resistivity is zero.

malawi_glenn
Homework Helper
That is not related to my question. I asked why the resistivity is zero.
That is true, and perfect diamagnetism aries due to SC, not vice versa.

But is the resisvitiy zero? I thought it was 10^-19 or similar?

ZapperZ
Staff Emeritus
2018 Award
That is not related to my question. I asked why the resistivity is zero.
Have you read the Tinkham text that was recommended?

The formation of Cooper pairs in the superconductor results in the condensation similar to a Bose-Einstein condensation for these pairs. When this occurs, all those pairs are in a single coherent state that can maintain such coherence over a very long range (think of a state with a sum of plane waves). This long-range coherence means that these pairs are "everywhere all the time". So the naive picture of this is that this is what causes the supercurrent to move with no resistance.

Zz.

diamagnetism arises from superconductivity?

That is true, and perfect diamagnetism aries due to SC, not vice versa.
why would you think that diamagnetism arises from superconductivity?

Cooper pairs

Have you read the Tinkham text that was recommended?

The formation of Cooper pairs ...is what causes the supercurrent to move with no resistance.

Zz.
and why do you suppose the electrons form pairs in the first place?

malawi_glenn
Homework Helper
Diamagnetism is due to the electrons "motion" in a solid. The electrons in a SC is coupled by cooper pairs (BCS theory). So the perfect diamagetism is due to the electrons in a SC, electrons affects the paramagnetism, not vice versa. The cause is before its manifestations. Diamagnetism and resistance are things that are related to how electrons are beeing transported in a solid.

Have you studied Solid State physics/ theory?

You dont seem to think scientific granpa, the Sun shines due to hydrogen fusion in its center followed by radiation transport. Not vice versa. Etc.

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spin not motion

Diamagnetism is due to the electrons "motion" in a solid. .
diamagnetism is due to electron spin not motion.

malawi_glenn
Homework Helper
diamagnetism is due to electron spin not motion.
Pauli paramagnetism are due to spin. Diamagetism are due to electrons orbits in the atoms.

Why didn't you answer my questions?

BCS theory and cooper pairs explains a lot and is one the greatest theories in modern physics. You are most welcome to try disprove it:)

Diamagetism are due the properties of electrons in a solid, a SC is a perfect diamagnet due to its special electron configurations. Diamagetism does not affect electrons, electrons affect diamagnetism.

malawi_glenn
Homework Helper
and why do you suppose the electrons form pairs in the first place?

The scientific method. You find a phenomena, try to dervie a physical theory that is consistent and can make predictions. If the predictions are found and are correct, the theory survices. BCS theory and cooper pairs have survived.

ZapperZ
Staff Emeritus
2018 Award
and why do you suppose the electrons form pairs in the first place?
Because the paring state has a lower energy than the single-particle state. This is what Leon Cooper showed for 2 electrons just above the Fermi energy, and what was extended in the BCS theory for the Fermi gas itself.

Zz.

electron orbits

Pauli paramagnetism are due to spin. Diamagetism are due to electrons orbits in the atoms.
.
electrons dont 'orbit' the nucleus.

i know that they form pairs

The scientific method. You find a phenomena, try to dervie a physical theory that is consistent and can make predictions. If the predictions are found and are correct, the theory survices. BCS theory and cooper pairs have survived.
i know that they form pairs. i am asking why (you think) the electrons form pairs.

malawi_glenn
Homework Helper
electrons dont 'orbit' the nucleus.
Of course they dont, not the classical way. You dont need to correct me on this point, i know these things very very well and I have never stated that they orbit like planets round the sun. The diamagnetism are due to the QM 'ortibs 'electrons have in atoms.

malawi_glenn
Homework Helper
i know that they form pairs. i am asking why (you think) the electrons form pairs.
Well that is what this tread is about, the OP asked why you have zero resistivity in SC, and where he can find litterature to study BCS etc. Then you said that they have zero resistivty due to diamagnetism, I said that you are not correct here.

Because the paring state has a lower energy than the single-particle state. This is what Leon Cooper showed for 2 electrons just above the Fermi energy, and what was extended in the BCS theory for the Fermi gas itself.

Zz.
i know that. the question becomes why do they not form pairs in materials that arent diamagnetic? what is different about diamagnetic materials?

Well that is what this tread is about, the OP asked why you have zero resistivity in SC, and where he can find litterature to study BCS etc. Then you said that they have zero resistivty due to diamagnetism, I said that you are not correct here.
diamagnetism is the tendency of the electrons to orient their spin opposite that of the magnetic field and thereby cancel it out. that is exactly what electrons in cooper pairs are doing therefore i believe that diamagnetism (or whatever causes diamagnetism) is what causes electrons to form pairs.

ZapperZ
Staff Emeritus