A Stability of persistent currents in superconductors regardless of temperature

[maxpi]

Thanks for clarifying! So the lifetime experiments are still proposals - that makes sense. It's indeed surprising how little work has been done on systematic decay measurements, given how fundamental they are.

Regarding your macroscopic rings (20 mm / 10 mm) - that's interesting because at those scales, you're firmly in the regime where my framework (TCTQ) predicts topology becomes negligible. The crossover scale d_c ~ 50-100 nm means topological effects only matter for nano-scale structures.

But here's where our perspectives might connect: you're asking about *pair permanency* (whether the same electrons stay paired), while I'm asking about *topological protection* (whether the pair wavefunction has conserved quantum numbers).

These might be related! If pairs have non-trivial Berry phase (topological winding number c₁ ≠ 0), then the phase coherence is protected by topology - not because the literal electrons are "permanent," but because the wavefunction can't continuously deform to the normal state without closing the gap.

**A concrete test to distinguish our frameworks:**

Your "permanent pairs" picture predicts that decay rate τ should be:
- Independent of ring size (if pairs are truly permanent)
- Sensitive only to defects/temperature

My TCTQ predicts:
- τ(d) ~ exp(E_top/kT) where E_top ∝ 1/d²
- Strong size dependence below d_c ~ 100 nm
- Negligible enhancement for macroscopic (mm-scale) rings

So if you measure τ for rings with wire diameter varying from 50 nm to 10 μm, we'd see:
- **Your prediction**: τ roughly constant (pair permanency is intrinsic)
- **TCTQ prediction**: τ enhancement only for d < 100 nm

This would definitively test whether topology matters for macroscopic currents!

**Regarding the "local states at BZ edges":**

I've been thinking more about your picture, and I think there's a deep connection to what topologists call "Wannier states" - maximally localized wavefunctions in a band. These naturally appear near BZ edges where Berry curvature peaks.

If you're interested, there are computational tools (Wannier90, WannierTools) that can extract these states from first-principles calculations. For Al, we could check:
1. Where in the BZ these "local states" concentrate
2. Their Berry phase (topological character)
3. How they couple to superconducting gap

This might bridge our languages - your "permanent electrons in local states" = my "electrons in topologically non-trivial Wannier orbitals."

**One more thought on the van Weerdenburg results:**

Even though you weren't involved, those data are publicly available and quite striking. The fact that Tc enhancement decays so rapidly (gone by ~3 nm) suggests the effect is surface-localized rather than bulk. This could support your idea about BZ edges being special - *at surfaces*, where symmetry is broken, those edge states might be enhanced.

If the community does eventually pursue your lifetime experiments, I'd be very interested in the results. And if you ever want to discuss the theoretical underpinnings (Berry phase, Wannier functions, etc.), I'm happy to share more details.

Thanks for the stimulating discussion - it's made me think more carefully about what "topological protection" really means at the microscopic level!

 

[Stanislav]

have you considered doing time-resolved measurements?

Would be interesting to do that. When the DC transport experiments confirm the expected current decay, then the time-resolution can clarify more details about the matter

 

[Stanislav]

how little work has been done on systematic decay measurements

It is because the eternal supercurrents cannot be explained by conventional theories

 

[Stanislav]

Regarding your macroscopic rings (20 mm / 10 mm)

The local states on BZ edges are large (~100 atoms), so nm-scales would disturb the large standing waves. Moreover, the interference of electron waves in the restrictions smaller than ~100 atoms will create fully new local states. My experiment proposal is rather about usual macroscopic effects in SC with local states not restricted by sample size, or restricted only in c axis as in experiments with 2D-Al .

 

[Stanislav]

But here's where our perspectives might connect: you're asking about *pair permanency* (whether the same electrons stay paired), while I'm asking about *topological protection*

Yes, if we consider the DOS-curve-form as preventing the transfer of new single electrons across the gap into the BZ edge and, thus, preventing the creation of new pairs, protecting the 'old' pairs against annihilation

 

[Stanislav]

but because the wavefunction can't continuously deform to the normal state without closing the gap.

Yes, because for the creation of new pairs some single electrons must thermally cross the gap and reach the BZ edge.

 

[Stanislav]

Your "permanent pairs" picture predicts that decay rate τ should be:
- Independent of ring size (if pairs are truly permanent)
- Sensitive only to defects/temperature

First - yes for scales much larger than the size of standing states (~ 100 atoms)
Second - rather no. Rather sensitive to the replacement rate of pairs with newly created pairs. Defects and T below Tc are not relevant for the dissipationless flow of condensate.

 

[Stanislav]

This could support your idea about BZ edges being special - *at surfaces*, where symmetry is broken, those edge states might be enhanced.

Yes. We must also take into account that at surface the electron density is smaller than in bulk, so for aluminum the SC gap may be larger than in bulk, although the pairing energy is roughly constant everywhere

 

[Stanislav]

- **Your prediction**: τ roughly constant (pair permanency is intrinsic)

τ roughly constant (pair permanency is intrinsic), but we can vary τ by artificial methods. For example, in a large isotropic SC ring we can create a small non-SC area (by local magnetic field). This non-SC area will reduce our τ due to pair creation/annihilation on the surface between SC and non-SC areas. The larger the surface the shorter τ. So we can show that the dissipationless flow is a consequence from the pair permanency.

 

[Stanislav]

I've been thinking more about your picture, and I think there's a deep connection to what topologists call "Wannier states" - maximally localized wavefunctions in a band. These naturally appear near BZ edges where Berry curvature peaks.

Yes, reasonbly to consider my local permanent states as a special case of Wannier states, when the Fermi surface is close to BZ edges. And Berry curvature peaks are also expected rather on BZ edges than anywhere else, since the local states may have their own DOS, different from usual Fermi spectrum.

 

[Stanislav]

- **TCTQ prediction**: τ enhancement only for d < 100 nm

For d<100 nm we must take into account new local states formed due to multiple wave function reflections from sample boundaries.