The resistivity of metals decreases with decreasing temperature–a result so ubiquitous that it is defining. But sometimes, the resistance of metals starts to increase at low temperature. In the early 1960s, it was shown that magnetic impurities were the cause of this upturn, and a few years later it was quantitatively explained by strong coupling between conduction electrons and the local magnetic moment of the impurity.

Suppose we take the original resistivity data of LK99 at face value. The plot from arXiv 2307.12037 is pasted below with digitized resistivity values at characteristic temperatures, in more conventional units for metals, written to the right. The resistivity starts off more than 20,000 micro-Ohm-cm. Too big to be called a metal. Maybe an insulator, maybe a semiconductor, maybe a (term I am coining now) garbage metal (bad and strange are already taken).

Superconductor or not, LK99 came out of left field. But one can say the same about the last three discoveries of high temperature superconductivity. Prior to the 1980s, superconductivity was mostly found in metals and intermetallic compounds, with Tc maxing out around 20K. Bardeen-Cooper-Schrieffer (BCS) theory and refinements thereof described most measured properties. In 1986, the world was shocked by superconductivity near 40K in copper-oxide (cuprate materials), which was skyrocketed to above 100K within short order.

Recently, some electronic structure calculations of LK-99 were posted. I will include expert critiques at the end of this 🧵, but for now, I want to discuss, what is a flat band and what does it have to do with superconductivity? TLDR: electronic structure calcs predict how electrons move in a crystalline solid in the non-superconducting state which affects almost every other electronic attribute. How/if this connects to superconductivity depends on the SC mechanism, and there is not always a connection