Why do superconductors superconduct current?

[Gerenuk]

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

 

[staf9]

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.

 

[Gerenuk]

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]

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.

 

[staf9]

f95toli's book is definitely a mathematically challenging explanation and should be what you're looking for, I'll give it one more shot too, perhaps this may be of help:

http://meso.phys.northwestern.edu/documents/quasiclassical.pdf"

 

[granpa]

because its diamagnetic

 

[malawi_glenn]

because its diamagnetic

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

 

[granpa]

i meant perfectly diamagnetic

 

[Gerenuk]

i meant perfectly diamagnetic

That is not related to my question. I asked why the resistivity is zero.

 

[malawi_glenn]

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]

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.

 

[granpa]

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?

 

[granpa]

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]

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.

 

[granpa]

spin not motion

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

diamagnetism is due to electron spin not motion.

 

[malawi_glenn]

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]

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]

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.

 

[granpa]

electron orbits

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

electrons don't 'orbit' the nucleus.

 

[granpa]

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]

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?

 

[malawi_glenn]

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.

 

[granpa]

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?

 

[granpa]

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]

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.

 

[granpa]

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?

 

[granpa]

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?

 

[ZapperZ]

Er.. did I have a weird deja vu, or didn't you just repeated yourself here?

Zz.

 

[ZapperZ]

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.

 

[granpa]

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.

 

[malawi_glenn]

The usual treatment of the diamagnetism of atoms and ions employs the Larmor theorem: In a magnetic field the motion of the electrons around a central nucleus is, to the first order in B, the same as a possible motion in the absence of B except for the superposition of a precession of the electrons with angular frequency:

[tex] \omega = eB/2mc [/tex]

This was from Kitell, diamagnetism is due to atomic electrons tending to loop around the applied B-field, i.e it is related to their orbital angular momenta. And they are orbiting so that the applied B field is canceled (not completley).

Paramagnetism is the tital Atomic spin J that wants to be allinged with the B-field.

Pauli paramagnetism is due to the conduction electrons intrinsic spin wanting to be allinged with the applied B-field.

Iam not going to write in this thread more, you are just annoying me grandpa. Cite scienfic litterature instead of coming with your non-sence speculations here. Superconductivity and diamagnetism are very well understood. You just seem to lack the basics.

Just read this:
"i know that. the question becomes why do they not form these cooper pairs in non-superconductors?"

Maybe becase cooper pairs gives you SC ?

 

[ZapperZ]

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.

No, if anyone is trolling, it appears to be you.

Where did I say that cooper pairs form in non-superconductors {even if there ARE recent results that show paring in insulators}? Are all materials that eventually become superconducting HAVE to be a diamagnet? High Tc cuprates are antiferromagnetic, save for the dopants.

The diamagnetism (or perfect diamagnetism) in superconductors occurs AFTER it has undergone such transition. Even then, this is not due to individual spins, but rather due to the whole superfluid responding to the external magnetic field. So I have no clue where this requirement for diamagnetism to be present FIRST before superconductivity can set in. Can you specifically point out in the BCS theory where this is required?

Zz.

 

[granpa]

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.

i am not suggesting that electrons simply form pairs and that causes diamagnetism and superconductivity.

if we think of each electron as a small magnet and if we could somehow cancel out the charge then the two electrons would indeed be attracted to one another and would couple with a certain amount of strength but the resulting pair would still have a magnetic field because the spins would be parallel. in cooper pairs the spins are opposite therefore the magnetic fields cancel out entirely. i assume therefore that the bonding is due to the same mysterious force that causes diamagnetic materials to generate magnetic fields that oppose and cancel out any externally applied magnetic fields. i don't see why the coupling strength would be the same for all superconductors.

 

[granpa]

No, if anyone is trolling, it appears to be you.

Where did I say that cooper pairs form in non-superconductors {even if there ARE recent results that show paring in insulators}? Are all materials that eventually become superconducting HAVE to be a diamagnet? High Tc cuprates are antiferromagnetic, save for the dopants.

The diamagnetism (or perfect diamagnetism) in superconductors occurs AFTER it has undergone such transition. Even then, this is not due to individual spins, but rather due to the whole superfluid responding to the external magnetic field. So I have no clue where this requirement for diamagnetism to be present FIRST before superconductivity can set in. Can you specifically point out in the BCS theory where this is required?

Zz.

i asked you why electrons form cooper pairs in superconductors and not in non-conductors. you never answered my question except to give a flippant response about it being a lower energy state (which is self-evident).

i am the one saying that diamagnetism comes first. that it causes the electrons to form cooper pairs.

 

[ZapperZ]

i asked you why electrons form cooper pairs in superconductors and not in non-conductors. you never answered my question except to give a flippant response about it being a lower energy state (which is self-evident).

I'm not being flippant. I thought by mentioning the Fermi energy, it is obvious that it requires charge charriers!

i am the one saying that diamagnetism comes first. that it causes the electrons to form cooper pairs.

Then you shouldn't be asking me about the diamagnetism requirment since this is your "model".

i am not suggesting that electrons simply form pairs and that causes diamagnetism and superconductivity.

if we think of each electron as a small magnet and if we could somehow cancel out the charge then the two electrons would indeed be attracted to one another and would couple with a certain amount of strength but the resulting pair would still have a magnetic field because the spins would be parallel. in cooper pairs the spins are opposite therefore the magnetic fields cancel out entirely. i assume therefore that the bonding is due to the same mysterious force that causes diamagnetic materials to generate magnetic fields that oppose and cancel out any externally applied magnetic fields. i don't see why the coupling strength would be the same for all superconductors.

Then you are formulating your own personal theory. You should also not ignore TRIPLET superconductors such as the ruthenates which completely destroys your scenrios of cooper pairs made up only of electrons with "opposite spins".

The "bonding" in conventional superconductors is due to phonons. You see the phonon coupling clearly in McMillen-Rowell reconstruction of in the tunneling density of states, in the electron-phonon coupling strength, and in the isotope effect (which you have not addressed).

Zz.