My current LK99 questions

Me: PhD in condensed matter experiment, brief read-through of the 3-person paper a few days ago, went and checked out the 6-person paper just now, read some other links as needed.

EDIT: If I'm reading their figure 4 correctly, I missed how impossible their magnetic susceptibility data was if not superconducting. My bad - I've sprinkled in some more edits as necessary for questions 1, 2, and 4.

Q1

One person alleges an online rumor that poorly connected electrical leads can produce the same graph.  Is that a conventional view?

Electrical leads can explain almost arbitrary phenomena. They measured resistivity with a four point probe, where you flow a current between two outer wires and then check the voltage between two inner wires. If the inner wires for some reason don't allow current to pass at small voltage (e.g. you accidentally made a schottky diode, a real thing that sometimes happens), that can cause a spurious dip in resistivity.

Alternatively:  If this material is a superconductor, have we seen what we expected to see?

The data isn't particularly clean, and there are several ways it differs from what you'd expect. Here's what a nice clean I-V curve looks like - symmetrical, continuous, flat almost to the limit of measurement below $T_c$, all that good stuff. Their I-V data is messier in every way. It's not completely implausible, but if it's real, why didn't they take some better-looking data?

Is the diminishing current capacity with increased temperature usual?

Yes, critical current changing with temperature is normal. In fact, if this is a superconductor, we can learn interesting things about it from the slope of critical current as a function of temperature, near the critical temperature (does it look like $\sqrt{T_c-T}$?).

 How does this alleged direct measurement of superconductivity square up with the current-story-as-I-understood-it that the material is only being very poorly synthesized, probably only in granules or gaps, and hence only detectable by looking for magnetic resistance / pinning?

The resistivity and levitation might be possible if only a tiny fraction of the material is superconducting, so long as there are 2D superconducting planes (a pattern that seems likely in a high-temperature superconductor) that can percolate through the polycrystalline material. However, I don't see how this would work with the apatite structure (also the Griffin DFT paper says the band structure is 3D, and the Cu-Pb chains of claimed importance are 1D), so I think it's more likely you would indeed have to have a high fraction of superconductor.

EDIT: I think their magnetic susceptibility data for sample 2, if correct, implies that the sample is at least 20% superconductor.

Q2

The video shows a surprising amount of diamagnetism, but it doesn't really look like the Meissner effect, and isn't so strong that it's impossible to explain without it (especially since most of the weight of the sample is resting on the magnet). Locking in place isn't strictly necessary, but especially in an impure material we should see a lot of pinning that prevents it from easily rotating. Russian catgirls are often untrustworthy.

EDIT: Actually, if I'm reading this right, figure 4a actually is pretty impossible without superconductivity. Score one for YES-Y. Although the data looks very ugly (where's the above-$T_c$ region with no diamagnetism?)

The diamagentism is still evidence that it's a superconductor! It's just even better evidence that it's a non-superconducting strong diamagnet. The moderate difference they show between field cooled and zero-field cooled magnetization curves is likewise evidence either that it's a superconductor, or evidence that it's an ordered diamagnetic material.

Q3

Somewhere between YES-X and NO-C. First, DFT calculations are a good starting point but always require a grain of salt. Second, I think calling this a "flat band" is overhyping it - the density of states enhancement that makes flat bands so hype-worthy isn't there as far as I can tell. Third, the hints of charge and spin waves in the material bear further study (if this is a superconductor they almost certainly are doing something interesting) but aren't all that surprising given that you've jammed a bunch of heavy atoms together in a nontrivial crystal structure.

Q4

If getting it to conduct current at 0 resistance is as easy as they make it sound, they've probably replicated it a hundred times in three different ways. However, what if it's tricky to get it hooked up to show superconductivity - you have to put the leads on just right, in some hard-to-understand way, and usually it doesn't look superconducting... then wishful thinking has a lot more room to operate.

EDIT: The extreme diamagnetism measurement for sample 2 could just be a calibration error on a sensitive measurement, requiring neither fraud nor superconductivity.

Q5

No idea. They clearly know physics. They're not maximally clear about everything, and I think they sweep data issues under the rug, but not in a way that makes me more suspicious conditional on the data.

I did a condensed matter experiment PhD, but high Tc is not my field and I haven't spent much time thinking about this. [Edit: I didn't see Charlie Steiner's comment until I had written most of this comment and started editing for clarity. I think you can treat this as mostly independent.] Still, some thoughts on Q1, maybe starting with some useful references:

Bednorz and Müller, "Possible High Tc Superconductivity in the Ba - La - Cu - O System" (1986) was the inciting paper for the subsequent discoveries of high-Tc superconductors, notably the roughly simultaneous Wu, Ashburn, Torng, et al. (1987) and Cava et al. (1987) establishing superconductivity in YBCO with Tc > 90K. The first paper is more cautious in its claims on clearer evidence than the present papers. The latter two show dispositive measurements.

I might also recommend Ekin's Experimental Techniques for Low-Temperature Measurements for background on how superconductors are usually measured (regardless of temperature). It discusses contacts, sample holders, instrumentation, procedures, and analysis for electrical transport measurements in superconductors, with a focus on critical current measurements. (I don't think skimming it to find a graph or statement that you can apply to the present case will be very helpful, though.)

One person alleges an online rumor that poorly connected electrical leads can produce the same graph.  Is that a conventional view?

It's well understood that a jump in the I-V curve does not imply superconductivity. Joule heating at high currents and thermal expansion, for example, can cause abrupt changes in contact resistance. I'm not sure exactly what it would take to reproduce that graph, but contact physics is gnarly enough that there's probably a way, together with other experimental complications.

If this material is a superconductor, have we seen what we expected to see?  Is the diminishing current capacity with increased temperature usual?

In the roughest sense, yes. The critical current density for a superconductor decreases as temperature increases and as magnetic field increases. Quantitatively, maybe. There are evidently other things going on, at least. (In another sense, the papers aren't really what I'd expect a lab that thought they had a new superconductor to present. But I think that can be explained between reproducibility issues, the interpersonal issues rushing publication, and the fact that they're somewhat outside the community that usually thinks about superconducting physics.)

How does this alleged direct measurement of superconductivity square up with the current-story-as-I-understood-it that the material is only being very poorly synthesized, probably only in granules or gaps, and hence only detectable by looking for magnetic resistance / pinning?

In an impure sample you would see high residual resistance below Tc (I think the authors do, but I'm not confident at a glance particularly given paper quality problems) and broad transitions due to a spread of transition temperatures over superconducting domains (it seems to me that the authors see very sharp transitions, although data showing the width in temperature from the April paper is omitted from the arXiv papers). The worse these are, the more mundane explanations are viable (roughly speaking), which is part of why observing the Meissner effect is important. But this is a good question. To some extent people are "vibing" rather than getting a story straight.

Curated.

Although the LK-99 excitement has cooled off, this post stands as an excellent demonstration of why and how Bayesian reasoning is helpful: when faced with surprising or confusing phenomena, understanding how to partition your model of reality such that new evidence would provide the largest updates, is quite valuable.  Even if the questions you construct are themselves confused or based on invalid premises, they're often confused in a much more legible way, such that domain experts can do a much better job of pointing to that and saying something like "actually, there's a third alternative", or "A wouldn't imply B in any situation, so this provides no evidence".

Me - Ph.D. in solid state materials chemistry.  Been out of the game for a while.  Less understanding of physics than some other commenters but have a different perspective that might be useful.

My first thought is that they have a minority phase; the samples are likely ~99% LK99 and ~1% unknown phase with weird properties.  You can see it in the video; part of the specimen is levitating but a corner of it isn't.  

The second thing I would do is try to make a bunch of variants with slightly different compositions to identify the minority phase.

The first thing I would do is try to make versions with different amounts of hydrogen.  Hydrogen is ubiquitous, diffuses readily into and out of most materials, and is invisible to most materials analysis techniques, but it can have a profound effect on a material's properties.  If you get different properties by annealing the sample under high-pressure hydrogen*, you're on the right track. 

*For safety's sake you would typically use forming gas, a non-flammable mixture of hydrogen with nitrogen (or sometimes argon).  Ammonia is also sometimes used but is more dangerous.

My background: educated amateur. I can design simple to not-quite-simple analog circuits and have taken ordinary but fiddly material property measurements with electronics test equipment and gotten industrially-useful results.

One person alleges an online rumor that poorly connected electrical leads can produce the same graph.  Is that a conventional view?

I'm not seeing it. With a bad enough setup, poor technique can do almost anything. I'm not seeing the authors as that awful, though. I don't think they're immune from mistakes, but I give low odds on the arbitrarily-awful end of mistakes.

You can model electrical mistakes as some mix of resistors and switches. Fiddly loose contacts are switches, actuated by forces. Those can be magnetic, thermal expansion, unknown gremlins, etc. So "critical magnetic field" could be "magnetic field adequate to move the thing". Ditto temperature. But managing both problems at the same time in a way that looks like a plausible superconductor critical curve is... weird. The gremlins could be anything, but gremlins highly correlated with interesting properties demand explanation.

Materials with grains can have conducting and not-conducting regions. Those would likely have different thermal expansion behaviors. Complex oxides with grain boundaries are ripe for diode-like behavior. So you could have a fairly complex circuit with fairly complex temperature dependence.

I think this piece basically comes down to two things:

1. Can you get this level of complex behavior out of a simple model? One curve I'd believe, but the multiple curves with the relationship between temperature and critical current don't seem right. The level of mistake to produce this seems complicated, with very low base rate.
2. Did they manage to demonstrate resistivity low enough to rule out simple conduction in the zero-voltage regime? (For example, lower resistivity than copper by an order of magnitude.) The papers are remarkably short on details to this effect. They claim yes, but details are hard to come by. (Copper has resistivity ~ 1.7e-6 ohm*cm, they claim < 10^-10 in the 3-author paper for the thin-film sample, but details are in short supply.) Four point probe technique to measure the resistivity of copper in a bulk sample is remarkably challenging. You measure the resistivity of copper with thin films or long thin wires if you want good data. I'd love to see more here.

If the noise floor doesn't rule out copper, you can get the curves with adequately well chosen thermal and magnetic switches from loose contacts. But there are enough graphs that those errors have to be remarkably precisely targeted, if the graphs aren't fraud.

Another thing I'd love to see on this front: multiple graphs of the same sort from the same sample (take it apart and put it back together), from different locations on the sample, from multiple samples. Bad measurement setups don't repeat cleanly.

My question for the NO side: what does the schematic of the bad measurement look like? Where do you put the diodes? How do you manage the sharp transition out of the zero-resistance regime without arbitrarily-fine-tuned switches?

Do any other results from the 6-person or journal-submitted LK papers stand out as having the property, "This is either superconductivity or fraud?"

The field-cooled vs zero-field-cooled magnetization graph (1d in the 3-author paper, 4a in the 6-author paper). I'm far less confident in this than the above; I understand the physics much less well. I mostly mention it because it seems under-discussed from what I've seen on twitter and such. This is an extremely specific form of thermal/magnetic hysteresis that I don't know of an alternate explanation for. I suspect this says more about my ignorance than anything else, but I'm surprised I haven't seen a proposed explanation from the NO camp.

Reading this post was one of the triggers for me mostly exiting the Manifold market (at a loss) - the trading is getting more serious, and I'm out of my depth.

It is still fun to spectate, though.

I have some very basic questions about the figure on display. It is the first time I look at this matter.

1. Is this the DC current-voltage curve of a sample of the material in question, without other shenanigans?
2. Is the "M" phase ohmic, i.e. current is proportional to voltage? It seems so to me by squinting at the graph, because it's 2-3 mV and 150-250 mA, but I'm not confident because it's in log scale without a grid.
3. Is the "N" phase ohmic too?
4. Are then the I, J, K, L phases superconducting?
5. Is also M superconducting? If it's a very short piece of metal, it seems realistic to me to get a resistance of 2 mV/150 mA = 13 mΩ (left M tip) without superconducting properties. So my impression is M = conductor, N = poor conductor, but I'm in doubt it could be M superconductor, N conductor.

purported video of a fully levitating sample from a replication effort, sorry I do not have any information beyond this twitter link.  But if it is not somehow faked or misrepresented it seems a pretty clear demonstration of flux-pinned Meissner effect with no visible evidence of cooling. [Edit] slightly more detail on video "Laboratory of Chemical Technology"

Had to look up what LK-99 is. Now I wonder, was this inspiration for

For those of you who don't know, room-temperature semiconductors would be a really big deal for all kinds of things, including AI alignment. 

Among many other applications, there is also a decent possibility of building affordable helmet-sized fMRI machines (the currently-giant machines that 3d-map electrical brain activity), enough for the living rooms of hundreds of alignment researchers (or even every smartphone), and get large sample sizes of hard data about what it physically looks like when humans succeed and fail at thinking about alignment. As in, hundreds of thousands of hours, of hundreds of people thinking about AI alignment, billions of 3d frames per year, including the hours and minutes leading up to every breakthrough that happened while someone was wearing the device (perhaps there will be a ding whenever a researcher is on the right track). 

That's the best thing I can currently think of. I have no idea what will be discovered by the thousands of actual ML engineers and neurologists who actually get to look at that kind of data (and see what they can do with it).

GPT4 confirms for me that the Meissner effect does not require flux pinning: “Yes, indeed, you're correct. Flux pinning, also known as quantum locking or quantum levitation, is a slightly different phenomenon from the pure Meissner effect and can play a crucial role in the interaction between a magnet and a superconductor.

In the Meissner effect, a superconductor will expel all magnetic fields, creating a repulsive effect. However, in type-II superconductors, there are exceptions where some magnetic flux can penetrate the material in the form of tiny magnetic vortices. These vortices can become "pinned" in place due to imperfections in the superconductor's structure.

This flux pinning is the basis of quantum locking, where the superconductor is 'locked' in space relative to the magnetic field. This can create the illusion of levitation in any orientation, depending on how the flux was pinned. For instance, a superconductor could be pinned in place above a magnet, below a magnet, or at an angle.

So, yes, it is indeed important to consider flux pinning when discussing the behavior of superconductors in a magnetic field. Thanks for pointing out this nuance!”

I think Sabine is just not used to seeing small pieces of superconductor floating over large magnets. Every Meissner effect video that I can find shows the reverse: small magnets floating on top of pieces of cooled superconductor. This makes sense because it is hard to cool something that is floating in the air.