The 1/4 occupied O atoms induced ultraflat band and the one dimensional channels in the Pb$_{10-x}$Cu$_{x}$(PO$_4$)$_{6}$O$_{4}$ (x=0,0.5) crystal

TL;DR

This study uses density functional theory to explore how oxygen vacancies and copper doping in lead apatite influence flat bands and one-dimensional channels, which are key to potential room-temperature superconductivity.

Contribution

It reveals the formation of one-dimensional channels induced by fully occupied oxygen atoms and how Cu doping affects the electronic structure of lead apatite.

Findings

Flat bands appear in undoped lead apatite and vanish with oxygen vacancies.

Cu doping creates one-dimensional channels that may facilitate superconductivity.

Oxygen vacancies and Cu doping significantly alter the electronic properties.

Abstract

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.