What happens when you have 1000V positive or negative charge on the conductor (let's take Mercury as an example) above Tc and then cool that charged conductor below Tc? Will it still be charged afterwards? Can this have an affect on the superconductivity? In the extreme case let us even assume we can deplete or add significant percentages of the charge carriers (1%) surely this will affect superconductivity significantly?
1000V below Tc may create critical current in the superconductor, so the SC state may disappear. Below the critical current the mercury conducts without resistance and the voltage on the sample is zero.
When we deplete or add carriers, Tc may become stronger or weaker (like a Tc dome in cuprates, where the doping modifies the carrier density).
Stanislav Dolgopolov I don't fully understand your answer, if the voltage on the sample is zero, doesn't that mean the charges have "disappeared"? Surely they must go somewhere? Do they get pulled into the bulk or ejected from the surface? As for adding 1% charge carriers, I wasn't referring to doping which is usually a bulk effect but rather a (theoretical) surface charge depletion/addition due to high voltage.
Stanislav Dolgopolov Adding to that, if we generate a critical current from the 1000V, this should generate an accompanying large B field, which would be measurable. If that is the case, is there any literature describing this effect? Furthermore, assuming we have an isotropic sphere with negative charge 1000V, in which direction does the current flow below Tc and in which direction will the magnetic field point?
If the voltage on the sample is zero, then the charges flow without resistance across the sample and into the further circuit (of course if the circuit is closed).
And of course if the electromotive-force in the circuit is present.
I belive that the question was "Do electrical charge influent on Tc?" The point is free electrons concentration. There is nothing do with current. If any cirquit exists the charge will
disappear before the metal will be cooled.
Yes. The electron density is relevant for the pairing energy. When we deplete or add carriers, Tc may become stronger or weaker (like a Tc dome in cuprates, where the doping modifies the carrier density).
Stanislav Dolgopolov Evgeny. Yu. Klimenko As mentioned earlier there is a distinction between bulk electron density which can be modified by doping and surface electron density caused by charging. Since the London penetration depth and the coherence length is often a surface-near effect (10-100 nm) for type I superconductors, I can imagine that that would lead to interesting size-effects (Similar to the way conventional ohmic theory breaks down when you decrease the width of a wire to below 100 nm and quantum mechanical and ballistic effects take over). In literature from 1960 I have found this particular experiment for thin films where charging has a small effect: Article Glover, R. E. & Sherrill, M. D. Changes in superconducting c...
But I still don't understand, does the electric field stay there when cooling below Tc? What happens when you substantially modify the surface of a superconducting sphere via charging?
Furthermore, I think it is difficult to compare this to doping because doping causes perturbations within the crystal lattice which can also have long-range effects (up to 100nm) and cause electron–dopant scattering which can also affect superconductivity. Pure surface charging on the other hand shouldn't create such artifacts.
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