Why do superconductors superconduct current?

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Discussion Overview

The discussion centers on the phenomenon of superconductivity, specifically addressing the question of why superconductors exhibit zero electrical resistance. Participants explore various theoretical frameworks, including BCS theory and the role of Cooper pairs, while also seeking recommendations for literature that provides a rigorous mathematical treatment of the subject.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the theoretical basis for superconductors having zero resistance and expresses a desire for a derivation from microscopic principles.
  • Several participants recommend various texts, including Tinkham's "Introduction to Superconductivity" and de Gennes' work, as resources for understanding superconductivity.
  • There is a discussion about the relationship between diamagnetism and superconductivity, with some participants asserting that perfect diamagnetism arises from superconductivity, while others challenge this view.
  • One participant explains that the formation of Cooper pairs leads to a coherent state that allows supercurrents to flow without resistance, likening it to Bose-Einstein condensation.
  • Another participant questions the reasoning behind why electrons form pairs in superconductors and what distinguishes diamagnetic materials from others in this context.
  • Disagreement arises regarding the role of diamagnetism in the formation of Cooper pairs, with some asserting that diamagnetism is a consequence of superconductivity, while others argue for a more complex relationship.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between diamagnetism and superconductivity, with no consensus reached on whether diamagnetism is a precursor to superconductivity or a result of it. The discussion remains unresolved regarding the specific conditions under which Cooper pairs form in different materials.

Contextual Notes

Participants reference various theoretical frameworks and texts, indicating a reliance on complex mathematical treatments. There are unresolved questions about the assumptions underlying the relationship between diamagnetism and superconductivity, as well as the conditions necessary for Cooper pair formation.

Gerenuk
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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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Superconductivity of Metals and Alloys
By Pierre-Gilles de Gennes

http://books.google.com/books?hl=en&lr=&id=ZMf_ticFcWYC&oi=fnd&pg=PA1&dq=superconductivity&ots=fOzOnYP6-Z&sig=VCvyDtYiGZFbT1BGnEq5_2wJSrs#PPP1,M1"

This may help.
 
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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?!
 
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
 
granpa said:
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
 
granpa said:
i meant perfectly diamagnetic

That is not related to my question. I asked why the resistivity is zero.
 
  • #10
Gerenuk said:
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?
 
  • #11
Gerenuk said:
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.
 
  • #12
diamagnetism arises from superconductivity?

malawi_glenn said:
That is true, and perfect diamagnetism aries due to SC, not vice versa.

why would you think that diamagnetism arises from superconductivity?
 
  • #13
Cooper pairs

ZapperZ said:
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?
 
  • #14
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 don't 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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  • #15
spin not motion

malawi_glenn said:
Diamagnetism is due to the electrons "motion" in a solid. .

diamagnetism is due to electron spin not motion.
 
  • #16
granpa said:
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.
 
  • #17
granpa said:
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.
 
  • #18
granpa said:
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.
 
  • #19
electron orbits

malawi_glenn said:
Pauli paramagnetism are due to spin. Diamagetism are due to electrons orbits in the atoms.
.

electrons don't 'orbit' the nucleus.
 
  • #20
i know that they form pairs

malawi_glenn said:
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.
 
  • #21
granpa said:
electrons don't 'orbit' the nucleus.

Of course they dont, not the classical way. You don't 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.

I can't see why you never admit your misstakes here?
 
  • #22
granpa said:
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.
 
  • #23
ZapperZ said:
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?
 
  • #24
malawi_glenn said:
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.
 
  • #25
granpa said:
i know that. the question becomes why do they not form pairs in materials that arent diamagnetic? what is different about diamagnetic materials?

Er... they don't? I'm not sure where this requirement for diamagnetism as the precursor to superconductivity comes from. I never made such statement.

Zz.
 
  • #26
malawi_glenn said:
Of course they dont, not the classical way. You don't 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.

that doest explain why you think that superconductivity causes diamagnetism. how does superconductivity effect electron spin?
 
  • #27
ZapperZ said:
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 these cooper pairs in non-superconductors?
 
  • #28
Er.. did I have a weird deja vu, or didn't you just repeated yourself here?

Zz.
 
  • #29
granpa said:
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.

If this is true, then the paring strength of ALL superconductors would be the same, because it only depends on the spin-spin coupling strength. We know that this isn't true, and that there is a wide range of coupling strength simply based on the size of the energy gap in tunneling spectroscopy. Furthermore, you would have an interesting time reconciling that scenario with the isotope effect.

Zz.
 
  • #30
ZapperZ said:
Er... they don't? I'm not sure where this requirement for diamagnetism as the precursor to superconductivity comes from. I never made such statement.

Zz.

you say that cooper pairs explain superconductivity. are you now saying that they form in non-superconductors?

dont think that i don't know that i am being trolled.
 

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