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In a (say) circular superconducting loop which has a current initially induced in it, and without any further external influences, and at a temperature above 0 K and below the transition temperature, will the current flow forever (e.g. years ?).

Are there imperfections in practical superconductors (e.g. YBCO) that actually cause the superconductivity to not be exactly zero? Are there other loss mechanisms?

(Edit) to clarify the mechanisms I am wondering about:

  1. The carriers (pairs) are circulating around the loop (do they all go in the same direction (at the same speed), or do some (N+X) go clockwise and others (X) go anti clockwise to have a net of just $N $?). Since the carriers are localized, they will have a small effect on the generated magnetic field and flux. Won't these temporal variations in $B$ cause electromagnetic radiation and therefore a loss of energy?

  2. Notwithstanding @Stanislav's comment, at $T > 0 K$, there is a distribution of thermal energy levels in all the particles in the system; couldn't some of the 'high' energy particles destroy the superconductivity briefly locally? And would this cause a loss of energy?

  3. Even a metallic superconductor has grain boundaries; do these cause no degradation in the superconductivity?

  4. A ceramic superconductor can be quite non-uniform at the molecular scale. Does this make superconducting not 'perfect'?

I am asking these because while I understand superconductors conduct extremely well and usefully for practical applications, a superconductor with $R=0$ is quite a precise value of $R$ and perhaps there are actually loss mechanisms that might show up and be detectable over long time scales (years?).

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  • $\begingroup$ In reality the current is not continuous, and is made up of point charges, which experience radiation, and thus lose energy $\endgroup$
    – jensen paull
    Commented Aug 7, 2022 at 17:31
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    $\begingroup$ @jensenpaull Doesn't matter if electrons are point charges. Once they are in a macroscopic stationary state carrying a constant current density, no radiation loss is allowed. $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Commented Aug 7, 2022 at 18:03
  • $\begingroup$ Assuming no radiation loss is allowed (macroscopically ? -- are the carriers moving at a perfectly constant velocity ?), are there imperfections in real (e.g. Cu or YBCO) superconductors that still cause a (resistive ?) loss ? $\endgroup$
    – jp314
    Commented Aug 7, 2022 at 18:11
  • $\begingroup$ @GiorgioP in the limit as it becomes a constant current density no radiation is produced, in reality it will never become a constant current density $\endgroup$
    – jensen paull
    Commented Aug 7, 2022 at 21:14
  • $\begingroup$ Nothing's ever perfect, except in theoretical idealizations (which are presumably where the existing answers are coming form). People make superconducting cavities all the time, and they have quality factors of order $10^{10}$, not infinity. For some pointers, google the term "surface resistance". $\endgroup$
    – knzhou
    Commented Aug 16, 2022 at 16:51

4 Answers 4

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A supercurrent flows forever, since electron pairs in a superconductor form the Bose-Einstein-Condensate (BEC). In the BEC every boson has a minimum and quantized kinetic energy and, thus, cannot transfer their energy to other particles by arbitrarily small portions. So the bosons flow as long as there is no external energy exceeding the quant of the boson energy. Answer to point 2 (couldn't some of the 'high' energy particles destroy the superconductivity briefly locally ?). External 'high' energy particles can destroy the pairs briefly locally. In equilibrium, kinetic energies of internal particles are stationary (like energies in molecules and atoms), that is the high kinetic energies are linked to zero total momentum of every particle. Therefore observable excitations are only a few kT, which cannot destroy pairs below Tc. Note, the thermal distributions at low Tc are rather quantized than smooth, so thermal excitations are rather a few kT than much larger values.

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  • $\begingroup$ but there is still thermal energy in the system (with a distribution) -- so can that occasionally split a pair ? would it recover ? $\endgroup$
    – jp314
    Commented Aug 16, 2022 at 18:52
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    $\begingroup$ Very good question. Indeed, there are two (thermal) energies: one splits the pair (say kT*), the second one breaks the Bose-Einstein-Condensation (say kTbec). In metals, usually, T*<Tbec, so the energy kT* splits the pairs at Tbec and there is no any BEC above T*. Above T* the pairs recombinate very fast, so the state is not a bosonic liquid, but rather a Fermi sea of free electrons. Thus, in superconducting metals kT* is the energy quant, breaking the supercurrent due to boson breaking. $\endgroup$
    – Stanislav Dolgopolov
    Commented Aug 17, 2022 at 5:48
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The basic idea is that for a superconductor the state of least energy can have a non-zero current. If this is already a state of least energy then there is no further lower-lying state for it to decay to. Loss mechanisms (in the sense of energy loss) therefore do not matter. So if the material is not subject to some external shock such as something falling on it or heating it up then yes the current can flow forever without the need for any energy input.

In practice such a current will not last forever because of other considerations: the material might be heated up because it was left in an ordinary room and the refrigeration failed owing to a power cut, or maybe it gradually underwent chemical reactions or a change owing to natural radioactivity, etc.

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  • $\begingroup$ I am asking about a sensible current -- not minor (quantum ?) fluctuations. If the temperature is kept well below the transition temperature, and there are no external disturbances, does the current decay ? e.g. given that temperature is somewhat a statistical phenomenon, do small localized 'temperature' perturbations cause localized non-zero resistance regions and consequently resistive losses ? $\endgroup$
    – jp314
    Commented Aug 7, 2022 at 17:54
  • $\begingroup$ and not about physical changes (chemical, radioactivity; loss of refrigeration). For instance a piece of Copper, or a YBCO superconductor (perhaps the behaviours are different ?). $\endgroup$
    – jp314
    Commented Aug 7, 2022 at 18:09
  • $\begingroup$ @jp314 Compare a superconductor with nonzero current in its ground state with iron, which has nonzero magnetization in its ground state. Bulk iron may slowly demagnetize, but that happens as the boundaries between completely-magnetized "grains" migrate to minimize the energy stored in the external magnetic field. A small iron crystal with no defects is spontaneously magnetized in its ground state, and will stay that way. $\endgroup$
    – rob ♦
    Commented Aug 7, 2022 at 18:14
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    $\begingroup$ But that example of a small iron crystal is just for a single non-zero value of magnetization. A superconducting loop could have any of a (nearly ?) continuum of values of current flowing. $\endgroup$
    – jp314
    Commented Aug 21, 2022 at 16:42
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You say "temperature above 0K", however any superconductor losses the superconductivity properties above a certain temperature. If the material is a superconductor and you induce a current initially, then the current will flow for a transient time. Then the temperature may change the material because of the random generation of rogue waves. Then if the system is large enough to neglect this molecular change, then the current is unaffected, if is not large enough, then the current may decrease.

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Sometimes it helps to think unconventionally. Let's assume that the electric current not only generates a magnetic field, but also aligns the magnetic dipoles of the subatomic particles with this macroscopic field. We keep the electric current small and thus do not disturb the cryogenic cooling. After a certain time, the magnetic dipoles of many subatomic particles are aligned in such a way that a self-holding (like a permanent magnet) occurs. Now we can switch off the circuit.

What can happen? If the temperature increases, the thermal movements of the subatomic particles and (Currie temperature) predominate and the magnetic dipoles move chaotically, the common magnetic field collapses and a Lenz current destroys the coil.

What else can happen? An external magnetic field brings the magnetic field of the ultracold coil out of its self-hold, a Lenz current occurs and destroys the coil.

What else argues for the self-holding of aligned magnetic dipoles rather than a lossless orbiting stream of Cooper electrons? In the production of superconducting wires, its difficult-to-roll material is embedded in copper and then rolled into micrometre-fine wires. In the process, it cannot be ruled out at all that the superconducting material forms continuous conductors at all. Nor is this important. What is important is to wind materials with unpaired electrons, which tend easily to self-hold the induced magnetic field, into magnetic coils and to minimise the thermal movements of the unpaired electrons.

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