# AC skin effect in superconductors

J

#### Jamie M

Jan 1, 1970
0
Hi,

Do any types of superconductors maintain zero electrical resistance
as the AC frequency goes up? I was thinking about applications using
panels:

http://phys.org/news/2013-02-patented-technique-key-solar-power.html

Would it be possible for a superconductor to efficiently conduct THz and
higher frequencies, I guess the current density will go up as the
electrons get compressed on the surface, is that the limiting factor?

Also is there a type of superconductor that only is superconductive on
the surface, similar to how a topological insulator only conducts
electricity on its surface?

cheers,
Jamie

W

#### whit3rd

Jan 1, 1970
0
Do any types of superconductors maintain zero electrical resistance
as the AC frequency goes up?

Not really. Some linacs use superconductive resonators (resonant microwave
cavities) that consist of thin lead plate on copper, that have very high
Q at microwave frequencies, but it isn't infinite. Superconductors have some AC
resistivity (or equivalent, there's energy losses).

J

#### Jamie

Jan 1, 1970
0
John said:
The niobium resonators at Jefferson Labs, the electron accelerator, have
unloaded Qs around 1e8. Their limit on RF power is arcing, from electrons and
ions being ripped out of the metal.
Sure, our place of employment does that all week long and many times on
the weekends.
But we try to avoid the arcing part

Jamie

N

#### [email protected]

Jan 1, 1970
0
The niobium resonators at Jefferson Labs, the electron accelerator, have
unloaded Qs around 1e8. Their limit on RF power is arcing, from electronsand
ions being ripped out of the metal.

Are superconductors unusually reflective at optical frequencies?

Mark L. Fergerson

M

#### Mr Stonebeach

Jan 1, 1970
0
Do any types of superconductors maintain zero electrical resistance
as the AC frequency goes up?

No, there is a loss component at any frequency above dc. As
a rule of thumb, the resistivity approaches the ballpark of the
non-superconductive metal resistivity at the 'gap frequency',
which for niobium is roughly 700 GHz. Below the gap frequency
the conductivity increases IIRC ~ 1/f^2, which means that the
losses become pretty damn small quite quickly as the frequency
is lowered.

There are materials with higher gap frequency, e.g. NbTiN
is used in SIS mixers at >1 THz.

More exotic materials such as YBCO show even higher
gap frequency, but they are a bit messy. They don't obey the
BCS theory, so they are not understood as well as the ordinary
superconductors. Their gap is typically not isotropic so that
the gap frequency is different depending on the direction of
the field components w.r.t the lattice planes.
Also is there a type of superconductor that only is superconductive on
the surface, similar to how a topological insulator only conducts
electricity on its surface?

All superconductors carry the current on their surfaces
only, that is the distribution which minimizes the magnetic
energy. But this is not the same thing as "being superconducive
only at the surface". The effect has the same mechanism behind
it as the ordinary skin effect, except that (i) it kicks in
already at zero frequency, because the material conductivity
is infinite; and (ii) the thickness of the current-carrying
layer is not zero, but rather it equals the so-called London
penetration depth (~90nm in Nb).

Regards,
Mikko

M

#### Mr Stonebeach

Jan 1, 1970
0
Are superconductors unusually reflective at optical frequencies?

No, they are extremely reflective only up to the gap frequency,
which is below 1 THz for most ordinary superconductors. If someone
in interested in details, the SC behaviour in the vicinity of the gap
frequency is described by the Bardeen-Mattis theory.

Regards,
Mikko

T

#### Tim Williams

Jan 1, 1970
0
Mr Stonebeach said:
No, they are extremely reflective only up to the gap frequency,
which is below 1 THz for most ordinary superconductors. If someone
in interested in details, the SC behaviour in the vicinity of the gap
frequency is described by the Bardeen-Mattis theory.

Is that analogous to the plasma frequency in ordinary metals? Which I've
heard is about where they start absorbing (most in the UV, except copper
among others, which, as we know, looks pink because it's not such a great
conductor up around blue). Eyeballing, is it coincidence that it's on the
order of kT/q, I suppose taking T as the critical temperature?

Interesting (in your other post) that you say it's roughly 1/f^2 (two pole
lowpass ), whereas from gap theory (again, with ordinary materials) one
might expect, say, an exponential response or something. Actually, the
cutoff of ordinary materials isn't exponential with respect to frequency,
in fact I've measured it for two semiconductors... I'll dig through my
notes when I get back...

Tim

M

#### Mr Stonebeach

Jan 1, 1970
0
Is that analogous to the plasma frequency in ordinary metals?  Which I've

The plasma frequency is due to the 'slowness' of the Thomas-
Fermi screening, whereas the SC gap frequency is caused by photons
starting to break the electron pairs. I don't see a connection
offhand, but then again, maybe there is a way to visualize the
pairing mechanism in such a way that an analogy can be recognized.
conductor up around blue).  Eyeballing, is it coincidence that it's on the
order of kT/q, I suppose taking T as the critical temperature?

It is not a coincidence. The supercurrent is carried by paired
electrons, and you can break the pairs either by kicking them with
strong-enough photons or by thermal agitation. The required energy
is roughly the same in both cases.
Interesting (in your other post) that you say it's roughly 1/f^2 (two pole
lowpass ), whereas from gap theory (again, with ordinary materials) one

I think the 1/f^2 dependence comes from the two-fluid model, in
case you want to look it up.

Regards,
Mikko

T

#### Tim Williams

Jan 1, 1970
0
Mr Stonebeach said:
The plasma frequency is due to the 'slowness' of the Thomas-
Fermi screening, whereas the SC gap frequency is caused by photons
starting to break the electron pairs. I don't see a connection
offhand, but then again, maybe there is a way to visualize the
pairing mechanism in such a way that an analogy can be recognized.

Hmm.. so to draw that analogy, one would have to know more about
Thomas-Fermi screening. Which I don't. I'll have to read up!

Now, by "break", does that actually mean a superconductor, say a
superconducting film, becomes less conductive and can be "broken" by
sufficiently intense light?

That would make sense from a different standpoint, namely: a sufficiently
intense B field is known to cause disruption (and, I would suppose, E as
well, though a sufficiently strong surface E field might simply not be
achievable in vacuum, i.e., it sparks first). If Bmax of "critical light
flux" coincides with critical field strength, it would be very
interesting. But then, such a classical explanation wouldn't depend on
frequency, either.

Ahh, physics...
It is not a coincidence. The supercurrent is carried by paired
electrons, and you can break the pairs either by kicking them with
strong-enough photons or by thermal agitation. The required energy
is roughly the same in both cases.

And, naturally, most stuff doesn't superconduct, because it's bathed
in...at least that much energy!
I think the 1/f^2 dependence comes from the two-fluid model, in
case you want to look it up.

Ah, the cutoff I was referring to:
http://www.seventransistorlabs.com/Images/SiGaAs_Atten.png
x axis is octaves in photon energy (i.e., log2(Ephoton), with E in eV), y
axis is attenuation in dB. Passband attenuation is due to reflection and
whatnot (0dB = no wafer in the apparatus). GaAs appears much sharper,
which I'm sure is something to do with density of states around the
bandgap or something like that. Evidently the silicon is ~100dB/octave,
or around 16 poles, a pretty sharp cutoff (not related to 1/f^2). A
pretty reasonable Butterworth filter, or something thereabouts.

Tim

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