${\mathrm{Pb}}_9{\mathrm{Cu}\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ is a charge-transfer semiconductor

By means of density functional theory and constrained random phase approximation we analyze the band structure of ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ (named LK-99). Our data show that the lead-phosphate apatite LK-99 in the proposed Cu-doped structure is a semiconductor with a predominant charge-transfer nature, a result incompatible with a superconducting behavior. In order to understand the interesting electronic and magnetic properties of this compound, it will be necessary to study the actual response to doping, the possibility of alternative structural and stoichiometric (dis)order, and to clarify the magnetic interactions as well as their impact on the electronic structure.

Figure 1

(a) Graphical representation of the crystal structure of ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ adapted from Refs. [6, 7]. The shadowed tetrahedra represents the PO4 units. Large spheres indicate Pb atoms, with the blue one showing the substitutional Cu site. Small spheres are oxygen atoms. The extra oxygen, disconnected from the PO4 tetrahedra, is displayed in black and labeled O1. (b) Band gap $E_g$ of ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ as obtained from $\mathrm{PBE}+U$ as a function of the on-site $U$ applied to the Cu-$d$ states The $\mathrm{PBE}+U$ data are obtained within the complex $\mathrm{DFT}+U$ implementation with (w) and without (w/o) SOC.

Figure 2

Band structure of FM ordered ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ at (a)–(c) PBE level (without $U$) and (d)–(f) $\mathrm{PBE}+U$ with $U=4.5$ eV and $J=0.8$ eV. For calculations not including SOC, the bands are decomposed over both spins components (up and down). The color code identifies the orbital character of the bands: Cu-$d$ orbitals are displayed in red whereas O1-$p$ orbitals are given in blue. Band structures obtained with other (cRPA) values of $U$ and $J$ are displayed in the SM (Figs. 6 and 7) [24].

Figure 3

Band structure of ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ at the $\mathrm{PBE}+U$ level including SOC for different values of $U$. The color code identify the orbital character of the bands: Cu-$d$ orbitals are displayed in red whereas O1-$p$ orbitals are given in blue. Through panels the transition from (a)–(d) metallic to (e), (f) CT insulator is observed.