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

Google books link

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:

Intro to quasiclassical theory

granpa

because its diamagnetic

malawi_glenn

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

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

malawi_glenn

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

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

why would you think that diamagnetism arises from superconductivity?

granpa

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

granpa

diamagnetism is due to electron spin not motion.

malawi_glenn

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

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.