One-Dimensional Superconductivity – Key Role of Defects Revealed by Quantum Chemical Calculations of Lead Apatite

Doped lead apatite has been recently reported to feature superconductivity at room temperature and ambient pressure, which may have huge impact on the progress of the humanity in general. Bulgarian researchers performing quantum chemical calculations support the one dimensional superconductivity case.

Georgi N. Vayssilov,* Petko St. Petkov,* Hristiyan A. Aleksandrov
Faculty of Chemistry and Pharmacy, University of Sofia, 1126 Sofia, Bulgaria

The first principle calculations, aiming at understanding the reasons for such behavior, suggest that reduced form of undoped and copper-doped lead apatite contain one dimensional channels, which are free of ions, but with electrostatic potential inside providing conditions for unimpeded electron mobility, potentially leading to superconductivity. Key aspect is that channels are surrounded by lead cations, which generate the necessary electrostatic field but due to their high atomic mass have reduced mobility and do not block the channels even at ambient temperature. Our observations on the modeled structures allowed us to present an alternative concept for features, giving rise of the superconductivity based on chemical understanding of the structure and frontier orbital of the material.

Part of the experimental research reports confirmed the results, reported by Lee et al., while the conclusion in other works are negative. Among other possible factors, this may be explained with different concentrations of the oxygen vacancies in the samples synthesized by different research group or, as suggested by Abramian et al., by different ration of fraction of the material with superconducting properties and non-superconducting material. The analysis presented here may suggest that materials with high concentration of oxygen vacancies may demonstrate higher superconductivity.

Conclusions
The results, reported in this work suggest that alternative understanding of the behavior of the LK-99 material based on the lead apatite, which is based on the previously acquired knowledge for the oxygen vacancies in reducible and non-reducible oxides. If the parent compound, lead apatite, is reduced via removal of the oxygens from the triangular channels of the structure, the obtained reduced material has a unique feature – channels, without atomic nuclei in it, but which have electron density inside due to electron pairs remaining from the removed oxygens. The lead cations, surrounding these channels, generate electrostatic potential inside them resulting in consequent alternation of HOMO and LUMO in the channel along the c axis of the structure, thus providing “highways” for electron motion in this direction.

In the case of copper-doped material the removal of the oxygens resulted in completely empty triangular channels since the remaining electrons reduce the Cu2+ cations to Cu+, as known for the reducible oxides. As in the case of the reduced lead apatite, the empty channels are surrounded by lead cations, which generate favorable electrostatic potential if additional electrons are provided. In this way, also in the case of reduced copper-doped lead apatite, the empty triangular channels may contribute to electron mobility along the c axis of the material.

According to our understanding, the general key factor for keeping the free space for electron mobility inside the triangular channel of the structure after removal of the oxygens even at high temperature, is that the channel is formed by lead cations. As described above, their first function is generation of electrostatic field inside the channel, but their second important feature is their high atomic mass, which limits the mobility of the cations themselves. Thus, even at room temperature the lead cations move with relatively small amplitude and do not block the channels.

In general, in this work we present an alternative concept for features, giving rise of the superconductivity based on chemical understanding of the structure and electronic properties of the material. Those features are: i) continuous space, e.g. channel, in the structure which is free from atoms in order avoid interference with electron mobility; ii) appropriate surrounding of this space by cations providing electrostatic potential that favors location of electrons inside the channel; iii) limited mobility of the cations, forming the channels walls in order to avoid blocking the free space due to their thermal motion. The latter feature may be accomplished by heavy cations as lead in the reduced lead apatite, presented above.