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The LK-99 hype came and went but the great potential of the apatite class of materials as platform for flat bands research must not be swept away in the process. A heuristic reinterpretation of the atomic structure of LK-99 is offered, including electronic signatures from the fully oxidized to the fully reduced. Here, copper is proposed to reside in the apatite channel rather than doping the Lead sublattice. Contact is made with the experimental x-ray powder diffractogram. The electronic signatures are found to reflect those of local [O-Cu-O] and [O-Cu-Vo**] molecular ions, where Vo** is a 2+ charged vacant oxygen site in the apatite channel. The local nature warrants flat bands. Charge carrier concentration is controlled by the oxygen content. Fully reduced LK-99 is a wide band gap insulator with a well-developed intermediate band. Fully oxidized LK-99 is a magnetic insulator, while the partially reduced LK-99 allows for hopping of holes between anti bonding pi orbitals of non-magnetic and magnetic [O-Cu-O] moieties. The findings are extended to include the case where half of the Cu atoms are replaced by Ni and half by Zn. For [O-Ni-O] +[O-Zn-Vo**] inter-site accidental near degeneracy among states at EF is reported, while for [O-Zn-O] + [O-Ni-Vo**] the near-degeneracy at EF on hole doping is among intra-site valence states exclusively on [O-Ni-Vo**]. The apatite platform is ideal for the study of flat bands associated phenomena. The reinterpreted fully reduced LK-99 system invites intrinsic intermediate band solar cells applications. Sites with variable oxygen occupation allow for holes doping, the consequences of which include strong correlations between electrons and lattice that suggest the emergence of (rebuilt) phonons mediated intra- as well as inter- bands (virtual) electron transfer-based phenomena, feeding the quest for ambient conditions superconductivity., Comment: 10 pages, 6 figures

An intuitive chemical perspective on the LK-99 material is outlined and supported by DFT calculations. A hidden flat Lead band that exhibits instability toward charge density wave formation is exposed. Electron transfer between Lead CDW/conduction bands and Cu$_3$d$^9$/Cu$_3$d$^{10}$ impurity states is suggested to embody the observed phenomenology reminiscent of room temperature superconductivity. The inter-system electronic instability is reflected in a chemical instability involving 2Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O => Pb$_{20-2x}$Cu$_{2x}$(PO$_4$)$_{12}$(O$_2$). Implications for tuning posttreatments as well as handling of the LK-99 material emerge., Comment: 6 pages, 3 figures

A random forest regression based supervised machine learning method to predict experimental critical temperature of superconductivity from the electronic band structure, as obtained from Density Functional Theory, is demonstrated. This complementarity between experiment and theory draws inspiration from the merging of Kohn-Sham and Bogoliubov-De Gennes equations [W. Kohn, W, EKU Gross, and LN Oliveira, Int. J. of Quant. Chem., 36(23), 611-615 (1989)]. Features in the Kohn-Sham Density Functional Theory band structure away from EF becoming decisive for the superconducting gap demonstrates this divide-and-conquer physical understanding. Not committing to any microscopic mechanism for the SC at this stage, it implies that in different classes of materials, different electronic features are responsible for the superconductivity. However, training on known members of a class, the performance of new members may be predicted. The method is validated for the A15 materials, including both binary A3X and ternary A6XY intermetallics, A=V, Nb, demonstrating that the two do indeed belong to the same class of superconductors., Comment: 12 pages, 4 figures and Supplementary Information containing 8 additional figures

Low-energy instabilities in the hole doped cuprates include, besides short range antiferromagnetic fluctuations and superconductivity, also ubiquitous translational and rotational symmetry breakings. The overwhelming majority of interpretations of these possibly related properties rely on mappings onto three bands spanned by the three atomic orbitals Cu3d(x2-y2)(sigma), O2px(sigma), and O2py(sigma), these three local orbitals spanning the Zhang-Rice band (ZRB), the lower Hubbard bands (LHB) and the upper Hubbard bands (UHB), respectively. Here we demonstrate by means of supercell Density Functional Theory (DFT) (a) how oxygen intercalation affects the structures of the buffer layers, and (b) how the attenuated crystal field pulls two additional oxygen bands in the CuO2 plane to the Fermi level. The self-consistent changes in electronic structure reflected in the corresponding changes in external potential comprise formal properties of the Hohenberg-Kohn theorems. Validation of present days' approximate exchange-correlation potentials to capture these qualitative effects by means of supercell DFT is made by comparing computed doping dependent structural shifts to corresponding experimentally observed correlations. The simplest generalization of Bardeen-Cooper-Schrieffer (BCS) theory is offered to articulate high critical temperature superconductivity (HTS) from a normal state where crystal field causes states related to two non-hybridizing bands to coalesce at EF., Comment: 18 pages, 1 table, 6 figures

A "super-atom" conceptual interface between chemistry and physics is proposed in order to assist in the search for higher TC superconductors. High-TC superconductivity HTSC is articulated as the entanglement of two disjoint electronic manifolds in the vicinity of a common Fermi energy. The resulting HTSC ground state couples near-degenerate protected local "super-atom" states to virtual magnons in an antiferromagnetic AFM embedding. The composite Cooper pairs emerge as the interaction particles for virtual magnons mediated "self-coherent entanglement" of super-atom states. A H\"uckel type resonating valence bond RVB formalism is employed in order to illustrate the real-space Cooper pairs as well as their delocalization and Bose Einstein condensation BEC on a ring of super-atoms. The chemical potential \mu(BEC) for Cooper pairs joining the condensate is formulated in terms of the super-exchange interaction, and consequently the TC in terms of the Ne\'el temperature. A rationale for the robustness of the HTSC ground state is proposed: achieving local maximum "electron correlation entropy" at the expense of non-local phase rigidity., Comment: 25 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1007.4115

Two Bi2201 model systems are employed to demonstrate how, beside the Cu-O \sigma-band, a second band of purely O2p\pi character can be made to cross the Fermi level owing to its sensitivity to the local crystal field. This result is employed to explain the particle-hole symmetry breaking across the pseudo-gap recently reported by Shen and co-workers, see M. Hashimoto et al., Nature Physics 6, (2010) 414. Support for a two-bands-on-a-checkerboard candidate mechanism for High-Tc superconductivity is claimed., Comment: 25 pages, 8 figures

A resonating valence bond RVB approach is taken to demonstrate formation of real-space Cooper pairs and High-TC superconductivity HTS. Non-adiabatic coupling between holes aggregates (super-atoms) and undoped anti-ferromagnet cause virtual excitations in either system due to inter-system coupling. HTS is said to reflect cooperative co-existence of two Bose-Einstein condensates in terms of one real-space Cooper pair condensate, and a second magnon condensate, which form at the same critical temperature. TC is formulated in terms of the super-exchange interaction. Connection is made to an equivalent real-space BCS formulation of HTS. Novel perspectives on the HTS in the electron-doped Sr1-xLaxCuO2 and Nd2-xCexCuO4 emerge., Comment: 25 pages, 4 figures

Shen et al. [1] recently reported on ARPES data from Pb-Bi2201 revealing both particle-hole symmetry breaking and pronounced spectral broadening, which they interpret to be indicative of spatial symmetry breaking without long-range order at the opening of the pseudogap. Here is demonstrated how their results could be interpreted to reflect static and dynamic inhomogeneous crystal fields causing inter-band transfer of holes upon cooling below T*. Possible relevance to formation of charge carrier inhomogeneities is discussed, and put in perspective of a proposed quantum chemical understanding of HTS., Comment: 18 pages, 8 figures