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lufc88
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Why is the magnetic field of a superconductor normally excluded?
lufc88 said:What causes these screening currents?
It's not really excluded. It's held constant. If you try to change the magnetic field, dB/dt induces an electric field, which cause currents through superconductor that cancel out the change in the magnetic field. This happens in any conductor, but in a normal conductor, there is resistance, so the screening currents die out, and eventually the field changes. In superconductor, these currents keep going, so the field inside never changes.lufc88 said:Why is the magnetic field of a superconductor normally excluded?
K^2 said:It's not really excluded. It's held constant. If you try to change the magnetic field, dB/dt induces an electric field, which cause currents through superconductor that cancel out the change in the magnetic field. This happens in any conductor, but in a normal conductor, there is resistance, so the screening currents die out, and eventually the field changes. In superconductor, these currents keep going, so the field inside never changes.
Naturally, the actual physics of how and why is a bit more complex and involves quantum mechanics. If you understand at least the Shroedinger's Equation, I can elaborate a bit more.
I see. I was somewhat confused over how the sueprconducting magnet works, leading me to believe that the field is "frozen in" rather than expelled. I'll have to take a closer look at the QM involved, though, I think I'm starting to see why it actually has to be zero rather than just constant.Dickfore said:No, B actually is zero in the bulk of the SC - Meissner effect. This is why perfect conductors differ from superconductors.
DrDu said:On a more abstract level, the expulsion of the magnetic field from a superconductor is due to the breaking of the U(1) gauge symmetry. Due to the Anderson-Higgs mechanism, the electromagnetic field becomes massive and therefore cannot enter far into the superconductor.
The Anderson Higgs mechanism was just recently confirmed in elementary particle physics with the detection of the Higgs boson. In a superconductor, the Cooper pairs correspond to the Higgs boson.
I wouldn't say so. Anderson derived the Anderson-Higgs mechanism in superconductors using random phase approximation to derive the current response to electromagnetic fields. The BCS hamiltonian is not gauge invariant and hence J=-QA cannot be derived from it. That's why Anderson (and others) was looking for a more elaborate microscopic description.Dickfore said:Yes, this is the explanation following from the Ginzburg-Landau phenomenological theory.
DrDu said:The BCS hamiltonian is not gauge invariant and hence J=-QA cannot be derived from it.
Dickfore said:I'm afraid I don't follow your logic.
DrDu said:However, the classical BCS explanation of the Meissner effect involves only single particle excitations, the reduced BCS hamiltonian does not even have collective excitations which could be described as a flow of Cooper pairs.
DrDu said:In a real superconductor there is a long range repulsive interaction between the electrons, namely the Coulomb interaction which gets collective excitations out of the gap.
That's why many people didn't believe the explanation of the Meisner effect of BCS.
I don't understand what you mean here. What collective modes? And how is screening supposed to work for "other modes" that it doesn't work for "these modes"?DrDu said:No, the finite energy of the plasmons (irrespective of in the superconductor or normal metal) is due to the long range of the Coulomb forces. Screening does not work for this kind of collective modes.
Yes, I remember reading his Nobel lecture. Let me emphasize once more that:DrDu said:The doubts on the validity of the BCS explanation of the Meissner effect spurred several important developments (I can give you references tomorrow).
For example Nambu wrote in his Nobel lecture ( http://www.nobelprize.org/nobel_prizes/physics/laureates/2008/nambu-lecture.html )
"I will now recall the chain of events which led me to the idea of SSB and
its application to particle physics. One day in 1956 R. Schrieffer gave us a
seminar on what would come to be called the BCS theory [5] of supercon-
ductivity. I was impressed by the boldness of their ansatz for the state vector,
but at the same time I became worried about the fact that it did not appear
to respect gauge invariance. Soon thereafter Bogoliubov [6] and Valatin [7]
independently introduced the concept of quasiparticles as fermionic excita-
tions in the BCS medium. The quasiparticles did not carry a definite charge
as they were a superposition of electron and hole, with their proportion
depending on the momentum. How can one then trust the BCS theory for
discussing the electromagnetic properties like the Meissner effect? It actually
took two years for me to resolve the problem to my satisfaction. There were
a number of people who also addressed the same problem, but I wanted to
understand it in my own way. Essentially it is the presence of a massless col-
lective mode, now known by the generic name of Nambu-Goldstone (NG)
LPN 2008 ekvationer...
boson, that saves charge conservation or gauge invariance."
Dickfore said:I don't understand what you mean here. What collective modes? And how is screening supposed to work for "other modes" that it doesn't work for "these modes"?
A superconductor is a material that can conduct electricity with zero resistance when cooled below a certain temperature, called the critical temperature. This is due to the formation of electron pairs, known as Cooper pairs, which move without any collisions with the atoms in the material, resulting in a perfect flow of electricity.
The exclusion of magnetic fields in superconductors is a result of the Meissner effect. When a superconductor is cooled below its critical temperature, it expels any magnetic fields that try to penetrate it. This is due to the perfect flow of electricity in the material, which produces a magnetic field that cancels out any external magnetic field.
The critical temperature is the temperature at which a material becomes a superconductor. It is an important parameter because it determines when a material can exhibit zero resistance and perfect conductivity. Superconductors must be cooled below their critical temperature in order to function.
Yes, there are certain types of superconductors, known as Type II superconductors, that can allow for the presence of a magnetic field. These materials have a higher critical temperature and can withstand stronger magnetic fields before losing their superconducting properties. However, they still exhibit the Meissner effect and expel magnetic fields up to a certain limit.
Superconductors have a wide range of potential applications, including in power generators, magnetic levitation trains, MRI machines, and particle accelerators. They can also be used in highly sensitive sensors and detectors, as well as in quantum computing research. The potential for zero resistance and perfect conductivity makes superconductors highly desirable for various technological advancements.