Electronic structure of the putative room-temperature superconductor Pb9Cu(PO4)6O

Another Density Function analysis of LK-99 proposed room-temperature superconductor by researchers at Northwest University in China and Tu Wien Austria Physics Institute. They think superconductivity might be possible, but only if LK-99 is doped, and that diamagnetism without superconductivity is unlikely.

Liang Sia,b and Karsten Heldb
a School of Physics, Northwest University, Xi’an 710127, China
b Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria∗

A recent paper [Lee {\em et al.}, J. Korean Cryt. Growth Cryst. Techn. {\bf 33}, 61 (2023)] provides some experimental indications that Pb10−xCux(PO4)6O with x≈1, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory calculations show lattice parameters and a volume contraction with x — very similar to experiment. The DFT electronic structure shows Cu2+ in a 3d9 configuration with two extremely flat Cu bands crossing the Fermi energy. This puts Pb9Cu(PO4)6O in an ultra-correlated regime and suggests that, without doping, it is a Mott or charge transfer insulator. If doped such an electronic structure might support flat-band superconductivity or an correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results.

A room temperature superconductor at ambient pressure would revolutionize the way we operate powerlines, how we build electric generators and electric motors. Already today superconductors are used in a billion-$ market, among others, to generate large magnetic fields, to connect power plants, as filters for mobile communication and as fuses for power plants.

What can we learn from the DFT calculations for prospective non-superconducting explanations of the experimental results of Pb9Cu(PO4)6O?

The sharp drop in resistivity might also occur from an ordering or structural transition, possibly affecting the lattice of the Cu dopants (at least when seeking to explain the low-T resistivity of the noise level not the 10−10 − 10−11 Ωcm stated in the LK99 paper). The putative Meißner effect and negative susceptibility could also result from a diamagnetic state. Here however our calculations provide some evidence against such a scenario. The narrow band(s) and the Cu 3d9 electronic configuration, indicate a (only slightly) screened spin- 12. A strong paramagnetic response can thus be expected. It is difficult to imagine how this can be overcome by a diamagnetic orbital response.

Th DFT calculations and consideration regarding correlation effects put Pb9Cu(PO4)6O in an ultra-strongly correlated regime, with U/W of O(10) instead of O(1) in cuprate superconductors because of the very narrow Cu band(s) crossing the Fermi energy. In such a situation the Coulomb interaction U clearly dominates over the kinetic energy and bandwidth W. This can give rise to flat-band superconductivity or a correlation enhanced BCS mechanism. A strong diamagnetic response is, on the other hand, not expected.

It is a bit puzzling, why Pb9Cu(PO4)6O with such a large U/W was not a Mott insulator or charge transfer insulator in experiment. A possible explanation is hole or electron doping through some off-stoichiometry in experiment. This would put Pb9Cu(PO4)6O into the class of doped Mott or charge transfer insulators. Cu doping x ̸= 1 will not change the Cu2+ oxidation state and the flatness of the bands. Additional Cu or Pb atoms or vacancies thereof would lead to some irregular arrangement and (spin) disorder potential. This is presumably bad for (super)conductivity. This puts O (or P) deficiency or excess as a possible source for such an accidental doping off-stoichiometry. Given the synthesis procedure also the replacement of O or P by S is conceivable. Against this background, it might be advisable to actively procure such a doping in the synthesis process, e.g. by controlling the O partial pressure or adding small amounts of a reducing or oxidizing agent.