  The search for room-temperature superconductors has been a long-standing goal
in condensed matter physics. In this study, we investigate the electronic and
geometric properties of lead apatite with and without Cu doped within the frame
work of the density functional theory. Based on our calculations, we found that
without the Cu doped the lead apatite shows an insulator character with flat
bands straddle the Fermi level. Once we introduce the O1 vacancies, the flat
bands disappear. Furthermore, we analyze the effects of Cu doping on the
crystal structure and electronic band structure of the material. Our
calculations reveal the presence of one-dimensional channels induced by fully
occupied O1 atoms, that are only 1/4 occupied in the literature, which may play
a crucial role in the realization of room-temperature superconductivity. Based
on our findings, we propose a possible solution to improve the quality of
superconductivity by annealing the material in an oxygen atmosphere. These
results contribute to a better understanding of the unusual properties of
Cu-doped lead apatite and will pave the way for further exploration of its
potential as a room-temperature superconductor.
