Consider a classical Hall bar, no quantum effects. If a magnetic field is applied the standard undergraduate treatment tells us that the Lorentz Force will lead to a build up of excess charge on one side of bar. This charge imbalance leads to a voltage between the two opposing sides, perpendicular to the current passing through the Hall bar. Now consider a superconducting bar deposited prepedincularly to the hall bar under consideration. If the magnetic field is smaller than the critical field, how does this superconducting strip influence the hall voltage/resistance? Let us assume that the proximity effects is negligble. The superconductor only covers part of the hall bar not all of it, there is ample bare Hall bar left, even after depositing the superconductor.
One line of reasoning of mine was, the superconductor simply shorts the potential difference, no excess charge is built up, end of story. $R_{xy}$ vanishes.
Another line of reasoning could be that the Meißner-Effect somehow weakens the magnetic field acting on the Hall-Bar at least locally. Finally, maybe this weakening is so small that it is irrelevant and everything is as before, the superconducting strip changes nothing, you can not actually shorten the Hall voltage.
Does anybody here have good experimental proof of what would happen? Or a convincing theoretical treatment? I have thought a bit about a Drude-Model but am unsure how to deal with a spatially inhomogenous situation such as this. I made some comparable measurements today but am not sure if my contacts were simply not good or if there really is no/next to no Hall voltage in this case.
