BenTC wrote:C
Could expand on this a bit. If the electric field is zero within the superconductor, how do you talk about increasing the "applied" electric field. Where is it applied to? I assume the increasing voltage would have to be taken up by the power supply internal resistance and the standard-cabling to the superconductor.
Thanks for this question: There is only one way in which an applied electric-field can be cancelled within a material, and that is by generating an opposite polarisation field. This happens in all conductors when you apply an electric-field without sending a current into the conductor. When, however, applying an electric field between two contacts a current flows precisely because the conductor attempts to cancel the applied electric-field; but owing to the current it can never achieve this.
Thus a material with "free" charge=carriers can never be a superconductor. In the low temperature metals the conducting electrons first have to go through a metal-insulator transition to form an array of localised anchored states. When applying an electric field these states polarise and cancel the electric field at each localised site. This increases their energy and they move up higher within the superconducting energy gap; which by the way forms fully at the critical temperature. In fcat if the latter does NOT happen (as modelled by BCS) one will NOT measure a sudden jump in the heat capacity of the electrons.
At higher temperatures these states can conduct a current by hopping conduction: i.e. by being kicked-on by temperature fluctuations. So there is still a resistivity: However, once their density becomes high enough at low temperatures, they can move by means of quantum fluctuations; as allowed by Heisenberg's uncertainty relationship.
Thus consider these localised "electron-orbitals": When injecting a charge at the injection contact it replaces one of them near the contact. This is possible since the orbital being replaced can borrow energy (delta)E and move to the adjacent site within an allowed time-interval (delt)t to replace the next orbital in the same manner. In this way charge is relayed through the superconducting phase. This is where the similarity with Newton's cradle comes in.
Now note that during each jump, the energy needed to do so is borrowed and returned. Thus there is no energy which requires dissipation and since the electric-field is cancelled by polarisation at each site, the current is not driven by acceleration. Thus no voltage difference can appear over the contacts. In fact even thermodynamics tells us that perpetual motion, which happens when the charge-carriers are flowing around a superconducting ring after trapping a magnetic flux, can only occur when you can obtain energy from a source, do work, change the work back in energy, and return it to the source. This is why superconduction relates to dark energy etc., as I have already mentioned above.
Thus to increase the current one must increase the applied electric-field: This increases the polarisation-energy of the localised states, which, in turn, decreases their density. Once their denisty becomes too low to allow jumping by means of quantum fluctuations superconduction stops: The maximum current is then reached.
It is late in South Africa and I am signing off to calm down before answering GIThruster above.