Current state of the LK-99 superconductor: Two failed replications and a promising new theoretical explanation

2023-08-01 13:19:55

The hot material, LK-99, promises to be a superconductor at room temperature and pressure; more than fifteen research groups are replicating this result. The first attempts, one Indian and one Chinese, are published on arXiv, both are negative: LK-99 is not a superconductor at room temperature. Both papers repeat the synthesis of Lee and Kim’s material, step by step, yielding an X-ray diffraction pattern very similar to theirs. However, the material obtained has very different electrical and magnetic properties. LK-99 is a semiconductor at room temperature; It does not present diamagnetism (so it does not levitate on a permanent magnet). But on social media many people are lauding a promising theoretical study published on arXiv; Using the VASP simulator based on density functional theory, the crystal structure of LK-99 is simulated. The electronic structure is observed to have flat bands (when the dopant copper replaces the appropriate lead ions, but not when it replaces the others). The hope of optimists is that early syntheses of LK-99 have failed to synthesize the proper material. Perhaps you have to build the material layer by layer, like van der Waals material, to get the crystal structure perfect. Although it must be remembered that the existence of flat bands does not imply superconducting states (in fact, it is not known if in bilayer graphene rotated with magic angle the flat bands are the key to superconductivity). We will have to wait for new replications, but everything points very badly. Sorry, for now, LK-99 is a dud.

As I already indicated in “My doubts about LK-99, the supposed superconductor at room temperature and pressure” (LCMF, Jul 26, 2023), the synthesis of Pb10-xCux(PO4)6O is very simple. The Chinese group has combined PbO and PbSO4 with 1:1 molarity in an oven at 725 °C for 24 hours to obtain Pb2SO5, which turns out to be a typical diamagnet. Then you have combined P and Cu with 1:3 molarity in an oven at 550°C for 48 hours to get Cu3P, which turns out to be a typical paramagnet. Finally, they combine Pb2SO5 and Cu3P with 1:1 molarity in a 925 °C furnace for 10 hours to obtain Pb2SO5, which turns out to be a typical diamagnet. Then you have combined P and Cu with 1:3 molarity in an oven at 550°C for 48 hours to get Pb10-xCux(PO4)6O, which turns out to be a typical semiconductor. While the Indian group uses the same synthesis protocol (with the only difference that PbSO4 is synthesized with the reaction Pb(NO3)2O+ Na2SO4 → PbSO4 + Pb(NO3)2O+ Na2SO4). For the rest, everything is the same, although they affirm that they have obtained Pb9Cu(PO4)6O, that is, LK-99 with x = 1. The X-ray diffractograms of both groups indicate that their material has a purity similar to that of LK-99. Lee and Kim, but it doesn’t levitate at room temperature; furthermore, it behaves like a paramagnet. The difference between the Indians and the Chinese is that the former have not measured the resistivity, since they consider that said measurement could be distorted by the measurement method.

The fact that the first two replication attempts that publish their results to arXiv have failed does not mean that the issue is resolved. But it points out that many other replication attempts will be published in a couple of weeks. For now, all indications are that LK-99 is not the holy grail of superconductivity. As a theorist he can only remember never say never again. The articles are Li Liu, Ziang Meng, …, Zhiqi Liu, “Semiconducting transport in Pb10-xCux(PO4)6O sintered from Pb2SO5 and Cu3P,” arXiv:2307.16802 [cond-mat.supr-con] (31 Jul 2023), two: (its format indicates that it has been sent to a journal of the group Nature); Kapil Kumar, N.K. Karn, V.P.S. Awana, «Synthesis of possible room temperature superconductor LK-99: Pb9Cu(PO4)6O,»  arXiv:2307.16402 [cond-mat.supr-con] (31 Jul 2023), two: https://doi.org/10.48550/arXiv.2307.16402; finalmente, el artículo teórico es Sinéad M. Griffin, «Origin of correlated isolated flat bands in copper-substituted lead phosphate apatite,» arXiv:2307.16892 [cond-mat.supr-con] (31 Jul 2023), doi: (has a format that points to an APS journal, perhaps Physical Review Letters).

I like the Indian article less than the Chinese one, which is much more careful and its reading is highly recommended. The results leave no room for doubt, at room temperature (300 K) and ambient pressure there is no trace of superconductivity. Furthermore, the resistivity increases as the temperature decreases between 300 K and 150 K, which is expected for a semiconductor. For an applied magnetic field of 1 millitesla no diamagnetic behavior is observed (as observed by Lee, Kim, and their co-authors), and for an applied field of 0.5 tesla paramagnetic behavior is observed. The Chinese group figures (shown here) leave no room for doubt; neither are the figures the Indian group. The only possible doubt about these two refutations is that the LK-99 material was not synthesized, but a very similar material from the point of view of the X-ray diffractogram.

Hope is the last thing you lose. The theoretical article by Sinéad M. Griffin (LBNL, Berkeley, California) offers us a ray of hope, albeit always with a pinch of salt. She has used the VASP software (Vienna Ab initio Simulation Package), based on density functional theory (DFT), to simulate LK-99 using a model that includes a Hubbard-U correction to account for the d-type electronic states of Cu dopant; she has used three values, U = 2, 4 and 6 eV, with the best results for U = 4 eV. Very flat bands associated with the dyz/dzz levels of Cu are observed around the Fermi level (in the figure the dashed black line with value 0.00, with the flat orange bands around it). These flat bands crossing the Fermi level are reminiscent of the flat bands in magic angle rotated bilayer graphene (MATBG). Griffin suggests that they can be interpreted as a sign that LK-99 might be superconducting. But beware, no one has shown that flat bands are essential for superconductivity in MATBG. In social networks there is some commotion about this theoretical result, but we must be very cautious, at least as much as Griffin in her own article. All he claims is that doped phosphate apatites are worth studying as a candidate for a superconducting material.

Much of Griffin’s article is devoted to confirming that the crystal structure he has used in the simulation corresponds to that of LK-99 (at least as reported in Lee and Kim’s articles). Two possible dopings have been simulated, the substitution of Cu in the Pb(1) lead ions, pink in the figure, as reported by Lee and Kim, and in the Pb(2) ions, purple in the figure; in the first case the flat d bands are observed, but in the second case they are not observed. Therefore, in the synthesis of LK-99 it is necessary to ensure that the lead ions are doped with copper in the proper position. What has surprised me the most is that, according to his calculations, it is 1.08 eV energetically more favorable that Cu ions replace Pb(2) than Pb(1) in doping. Perhaps therein lies the explanation for not being able to replicate the potential superconductivity of LK-99; perhaps the Indian and Chinese groups have obtained an LK-99 in which the Pb(2) have been doped with copper, instead of the Pb(1). This would be the only hope for those who profess blind faith in Lee and Kim. Perhaps its synthesis protocol hides some secret that favors the correct doping. That being said, never say never.