My understanding of the LK-99 science

# My understanding of the LK-99 science The original LK-99 synthesis involved a multi-step process of sealing powders in quartz tubes and letting them sit at high heat for hours. (This is what they refer to as the solid state method). While it theoretically gets baked out, one of the precursors contains sulfur. This will be important later. The authors argued based on crystallography data that this compound was Pb10CuX(PO4)6O. These crystals demonstrated two main effects: - A resistivity that appeared to drop suddenly to zero when the temperature was lowered below 127 C - Partial levitation above a permanent magnet These are indicators of superconductivity The authors attribute these effects to the material’s crystal structure. This proposed structure creates a “line” of Pb2 and O atoms because substituting copper for lead at various points in the crystal lattice causes everything to “tighten up” — copper is smaller than lead. The authors claim that this 1-D pattern is superconducting. (Note — MS Word preprints just look so much less profess) Let’s break down the claims: 1. LK-99 has the chemical makeup that the authors claim 2. LK-99 has the crystal structure that the authors claim 3. The levitation is due to the Meissner Effect* 4. The resistance goes to zero, not just close to zero 5. 3+4 are caused by the crystal structure creating a 1-D chain of superconducting atoms **What is the Meissner Effect?** There are ~4 effects that can cause something to float on a magnetic field: 1. Diamagnetism: a diamagnetic material responds to a magnetic field by creating an opposite magnetic field. 2. Ferromagnetism: a ferromagnetic material has a magnetic field that if oriented correctly will cause repulsion. (This is normal magnets!) 3. Meissner effect: superconductors “eject” magnetic fields, which cause forces away from it (I need to do the force diagram here but I think it has to do with loops of current on the surface of the superconductor that make sure that all magnetic fields cancel out. 4. Flux pinning: high temperature superconductors “pin” magnetic field lines that were present when they became superconducting. So the question is, what explains the observed effects? Then Sinéad Griffin published a paper using Density Functional Theory to show that the proposed structure could have “flat fermi level bands” that could give rise to superconductivity. The fermi level is the energy where you have a 50% chance of finding an electron. In an insulator it’s low, in a metal it’s high. In a semiconductor it’s different places. The bands of individual atoms get distorted by the atoms around them. The intuition (I believe) is that if the bands of a line of atoms are all the same, an electron can freely move between all of them — hence superconducting. The thing is that Density functional theory is a giant tower of assumptions. It can tell you that something is not impossible, not necessarily that it is possible. Then the labs with the big guns came in. The Schoop lab at Princeton synthesized it and used fancy X-ray diffraction to look at its structure and didn’t see a lot of copper. This suggests that it’s not this pure material — it has many phases. They also noted a basic fact that many of the crystals were transparent (which rules out superconductivity because it means all the electrons are bound). Finally they did fancier models (defect formation energy calculations) that show that the structure None of this *rules out* a bizarre situation but puts the burden of proof heavily in the camp of the superconductor believers. The last paper got the levitation effects but then were able to do magnetic measurements on the samples and tested its magnetization. Other people are pointing to Cu2S as the explation for the sudden drops in resistivity.  [Web URL for this note](http://notes.benjaminreinhardt.com/My+understanding+of+the+LK-99+science) [Comment on this note](http://via.hypothes.is/http://notes.benjaminreinhardt.com/My+understanding+of+the+LK-99+science)