They measured the resistivity of a pure Cu2S sample, a sample S1 containing 95% LK-99 and 5% Cu, and a sample S2 containing 30% LK-99 and 70% Cu2S.
The resistivity of the Cu2S sample has a drop of 3 to 4 orders of magnitude at about 390K (when temperature decreases). In the S2 sample the drop is much smaller, only factor 5. In S1 there is no such drop. Here the resistivity always falls with increasing temperature.
Then they write in the conclusion: "The superconducting-like behavior in LK-99 most likely originates from a magnitude reduction in resistivity caused by the first-order structural phase transition of Cu2S."
Since resistivity drop in LK-99 with temperature is about factor 10 according to https://arxiv.org/pdf/2307.12037.pdf Fig 5, that would mean that Sukbae Lee et al's specimen was composed of more than 70% Cu2S, which is unlikely.
The resistivity drop with decreasing temperature is not the only "superconducting-like behavior in LK-99". There is also a resistivity drop with decreasing current density and magnetic field at constant temperature. That cannot be explained with a phase change.
If the earth runs out of helium we will just use low field MRIs that don't require superconductors (see eg https://www.nature.com/articles/s41467-021-25441-6 ). Their resolution is lower than that of high field MRIs, but they still seem to be a useful diagnostic tool.
How do you explain the almost three orders of magnitude drop in resistance in Fig. 6d in one of the original articles ( https://arxiv.org/pdf/2307.12037.pdf ) with a few LK-99 particles sprinkled here an there? There must be a current path along which more than 99.8% of the material is in the supposed superconducting state. So the particles almost touch but not quite yet?
I think the more likely explanation is that the particles do touch each other but the interface is not superconductive. In other words, it is a polycrystalline material, and most of it is LK-99, but the grain boundaries are not a very good conductor. In conventional superconductors grain boundaries don't disrupt superconductivity because they are 3D superconductors, but in this allegedly 1D superconductor the superconducting channels in most cases don't meet at the grain boundaries, so the current has to overcome the resistance of some material that is almost an insulator.
If that is the case it will be difficult to produce a material that is macroscopically superconducting. But I hope researchers will be able to make single crystals that are large enough for resistance measurements so that finally it can be determined if this material is a superconductor or not. For practical uses the best result that can be achieved with this material may be a metal-LK-99 composite where the LK-99 particles lower the resistivity of the metal by 50-90%.
On page 4 they list two equivalent criteria for superconductivity: "the electric field criterion with 1 μV/cm or 0.1 μV/cm and resistivity criterion
with 10^-11 Ω·cm." On the same page they write: "In various bulk samples, specific
resistance was measured in the range of 10^-6 to 10^-9 Ω·cm." That does not meet the resistivity criterion, not even close.
In the second paper ( https://arxiv.org/abs/2307.12037 ) on page 8 they write: "In the first region below red-arrow C (near 60°C), equivalent to region F in the inset of Fig. 5, the resistivity with noise signals can be regarded as zero." I can only see from the plotted curve that the resistivity below 60°C is below about 5·10^-4 Ω·cm. Compare that to the resistivity of silver, which is 1.59·10^-6 Ω·cm.
It doesn't get better if you test the electric field criterion. On page 11 of the second paper you can see in Fig 6a that they measured a voltage of about 2mV in the "superconducting" state, and the voltage only drops off when the current approaches 0. In the first paper on page 19 they write that they used pogo probes with a distance of 1.2mm. So the electric field they measured is about 17mV/cm. That is a lot higher than the superconductor criterion of 1µV/cm, let alone 0.1µV/cm. Even if they mistakenly used mV instead of µV in their diagram, a factor of 17 would still need a good explanation.
So either a complete fake or an interesting effect but not superconductivity.
The resistivity of the Cu2S sample has a drop of 3 to 4 orders of magnitude at about 390K (when temperature decreases). In the S2 sample the drop is much smaller, only factor 5. In S1 there is no such drop. Here the resistivity always falls with increasing temperature.
Then they write in the conclusion: "The superconducting-like behavior in LK-99 most likely originates from a magnitude reduction in resistivity caused by the first-order structural phase transition of Cu2S."
Since resistivity drop in LK-99 with temperature is about factor 10 according to https://arxiv.org/pdf/2307.12037.pdf Fig 5, that would mean that Sukbae Lee et al's specimen was composed of more than 70% Cu2S, which is unlikely.
The resistivity drop with decreasing temperature is not the only "superconducting-like behavior in LK-99". There is also a resistivity drop with decreasing current density and magnetic field at constant temperature. That cannot be explained with a phase change.