Our finding, through calculation, of flat Cu-O bands at EF in Cu-doped Pb apatite show that this kind of system can be promising for superconductivity, though a critical aspect is whether or not the system will remain metallic, which is of course a requirement for supporting superconductivity. Our calculations indicate both challenges as well as possible paths for overcoming these challenges. First, we show that the system with exactly one Cu per cell (x=1) will be a metal only if the structure can maintain its relatively high P3 symmetry - and that it is generally unstable to a Jahn-Teller style symmetry lowering that opens a substantial gap at EF , turning the system into a charge-transfer insulator, which likely also has Mott-style correlations. Even though the structural changes are very modest between the symmetry-preserved and symmetry-lowered systems (bond angle changes maximum 1 degree), the electronic structure of the two are quite different, with the near-EF states of the latter showing significantly less Cu-O hybridization. Therefore, to support a metallic (and possibly superconducting) ground state in this system, at least one of two things must occur: (1) Some internal structural pressure must exist to maintain the higher P3 symmetry of the system, or equivalently, to disallow the energy-lowering distortion. This could in principle "protect" the flat bands at EF , keeping them available for supporting superconductivity. (2) A departure from the "pure" stoichiometry considered here would be necessary, for example by varying the concentration of O(4) atoms away from unity. Since the O(4) atoms are nominally 2- valence, a surplus of such O(4) atoms would act as a hole dopant or a deficit acting as an electron dopant. This could either lead to new impurity-like states within the band gap, or could shift the Fermi energy into the Cu-derived conduction band (electron-doped) or the PbO derived valence band (hope-doping). Such a scenario could potentially lead to a metallic flat-band state with interesting properties that should be explored by future experimental and theoretical studies. Assuming that such flat bands and their associated high density of states can be stabilized by the mechanisms discussed above, such bands could be strongly favorable for superconductivity. This is because bosons that might mediate electronic pairing are in general conducive to strong correlations from flat bands: for example the electron-phonon interaction can be greatly enhanced, and superconductivity mediated by spin fluctuations are also greatly enhanced by the flatness of the band; see for example Ref. [30]. Extremely flat states at the Fermi energy can also significantly enhance the electron-phonon coupling matrix elements, which would also support higher superconducting transition temperatures. In contrast with the hydride superconductors, the phonon modes are less violent for oxygen and copper and may not need high pressures to prevent the system from falling apart. The presence of disorder and flat electronic states together suggest the material may choose an s-wave superconducting phase. Most importantly, the Cooper pairing in that case will probably be better described by a strong coupling picture akin to the BEC limit where Tc/TF > 1/10. However, superconductivity is only one of many possible instabilities. It must compete with, e.g. magnetically ordered phases. An excellent illustration of this is CaFe2As2 : which is dominant depends on the details of the lattice structure [31]. Similarly, charge density waves can compete with the electron-phonon interaction, or possibly enhance it. It requires a more careful analysis of all possible competing instability-channels to explore what the material chooses as its ordered ground state. To summarize, we turn to Fig. 1. We have established that the weak hybridization and flat bands can lead to instabilities of different kinds (a) and (b). The pristine compound is a charge-transfer insulator, and appears to be robust against the disorder we have considered here. How a metallic phase forms from the near-EF states needs to be resolved by a combination of theory and experiment. The question of which boson predominates for correlated phenomena, including superconductivity, may well depend on the character of the metallic state. Note added: We are aware that works describing DFT studies of LK-99 have been posted on aXiv at similar time as our submission [18, 32]. We also need to note that need for a doping to achieve conductive state has been suggested very recently on the basis of DMFT calculations [33–35]. Prediction of half-metallic band structure for LK-99 has also been posted very recently [36]. A paramagnetic LK-99 that is not superconducting has also been realized in experiment [37].Recent experimental study of LK-99 states that room temperature superconductivity is very unlikely in this system [38] and observed transition might be related to the Cu2S impurity phase [39].


******너무 어려워서 요점만 내좆대로 발췌(볼드체)번역함. 내용 틀리거나 논지 틀리면 지적하셈.


구리로 도핑된 납 apatite는 이러한 시스템이 초전도성의 가능성이 있다는 것을 보여준다. 단, 그렇기 위한 조건으로, 이 시스템은 금속성으로 남아있느냐 매우 중요하다. // 그로므로, 금속성(즉, 초전도성의 가능성이 있는) 바닥 상태를 유지하기 위해, 다음 두 가지 중 하나가 필요하다. (1) 내부 구조의 압력으로 물질의 p3 구조가 유지되거나, 에너지준위를 낮추는 왜곡을 방지하여야 한다. (2) '순수한' 화학양론에서 벗어나는 것이 필요하다. 예컨데, O(4) 원자의 농도를 결합된 물질에서 감소시키는 등의. // 위와 같은 메커니즘에 의해 플랫 밴드와 그것과 관련된 high density of states는 안정화될 수 있으며, 이러한 밴드들은 초전도성이 발현되기에 아주 적당한 환경이다. // 그러나, 초전도성은 가능한 수많은 불안정한 상태 중 하나일 뿐이며, 그것은 다른 가능한 불안정한 상태, 예컨데 자기화된 상들과 경쟁적으로 발현될 것이다.

// 순수한 물질은 charge-transfer 절연체이며, 위에 고려한 불안정한 상태들과 완전히 배척되는 것으로 보인다. 금속상이 near-EF 상태에서 발생하는 지에 대해서는 이론과 연구를 통해 해결되어야한다. 



첨언 : 연구진은 우리가 논문을 제출할 당시 aXiv에 LK-99의 DFT 연구들이 게재되었음을 알고 있다. 우리는 DMFT 계산에 따라, 극히 최근에 도핑이 전류가 통하는 상태를 발생시키는데에 중요하다는 점을 중시하여야 한다. 초전도성이 없는, 반자성의 LK-99 역시 실험을 통해 관찰되었다. 최근, LK-99에 대한 실험적 연구들을 통해 이 물질계에서 상상초는 매우 가능성이 낮으며, 황화구리로 인한 상전이일 가능성이 논의되고 있다. 


[내 견해]


LK-99 스토리 라인, 특히 특허와 도핑에 대한 전개를 안다면, 이 논문이 출원된 특허와 비교해서 얼마나 유사한 것을 지적하는지 좀 신기할 것 같음.