Somebody knows the numeric value of electrons drift velocity in superconductors? How this value depends from the used superconductor material? What's about the current? Since the electrical resistance tends to zero, how many electrons can pass an area (a layer) that is occupied e.g. by 100*100 atoms?
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asked Jul 3, 2014 at 7:50
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$\begingroup$ Such value might depend on the electric field strength, doesn’t it? And what means “electrical resistance tends to zero”? Also, for your record, not only electors can drift. There are other things in semiconductors (and even such rare metals as beryllium) that can do it. $\endgroup$– Incnis MrsiCommented Aug 14, 2014 at 16:07
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$\begingroup$ @incnis mrsi: I'm more asking about is there im general a difference in electron speed between the drift velocity in a metallic wire and a superconductor. $\endgroup$– HolgerFiedlerCommented Aug 14, 2014 at 16:27
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$\begingroup$ In which conditions would you compare them? For the same current density the drift in a semiconductor will be much quicker because there are fewer carriers than in a metal. But for the same electric field strength the situation can be opposite. $\endgroup$– Incnis MrsiCommented Aug 14, 2014 at 16:34
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$\begingroup$ The answer was always present physics.stackexchange.com/questions/36053/… $\endgroup$– HolgerFiedlerCommented Dec 29, 2015 at 19:00
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1 Answer
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From:
Carver Mead's "Collective Electrodynamics" Section Magnetic Interaction of Steady Currents 1.11 Current in a Wire
Speaking of superconducting currents in a wire:
At long last, we can visualize the current distribution within the a superconducting wire itself. Because the skin depth is so small, the surface of the wire appears flat on that scale, and we can use the solution for a flat surface. The current will be a maximum at the surface of the wire, and will die off exponentially with distance into the interior of the wire. We can appreciate the relations involved by examining a simple example: A 10-cm-diameter loop of 0.1- mm-diameter wire has an inductance of $4.4*10^{-7} $ henry (p. 193 in Ref. 40). A persistent current of 1 ampere in this loop produces a flux of $4.4*10^{-7} $ volt-second, which is $2.1*10^8$ flux quanta. The electron wave function thus has a total phase accumulation of $2.1*10^8$ cycles along the length of the wire, corresponding to a wave vector $k=4.25*10^9 M^{-1} $. Due to the cyclic constraint on the wave function, this phase accumulation is shared by all electrons in the wire, whether or not they are carrying current.
In the region where current is flowing, the moving mass of the electrons contributes to the total phase accumulation. The 1-ampere current results from a current density of $6.4*10^{10} $ amperes per square meter flowing in a thin $“skin” \approx \lambda$ thick, just inside the surface. This current density is the result of the $10^{28} $ electrons per cubic meter moving with a velocity of $v \approx 20$ meters per second. The mass of the electrons moving at this velocity contributes $mv/ \hbar=1.7*10^5 M^{-1} $ to the total wave vector of the wave function, which is less than one part in $10^4$ of that contributed by the vector potential. That small difference, existing in about 1 part in $10^6$ of the cross-sectional area, is enough to bring $k$ and $A$ into balance in the interior of the wire.
The (p. 193 in Ref. 40) is from Fields and Waves in Communication Electronics by Simon Ramo, John R. Whinnery, Theodore Van Duzer
The velocity in this example is about 20 meters per second. The velocity has no dependence on the material as long as it is superconducting.
