Symmetry breaking induced insulating electronic state in Pb9_{9}Cu(PO4_4)6_6O

The recent experimental claim of room-temperature ambient-pressure superconductivity in a Cu-doped lead-apatite (LK-99) has ignited substantial research interest in both experimental and theoretical domains. Previous density functional theory (DFT) calculations with the inclusion of an on-site Hubbard interaction $U$ consistently predict the presence of flat bands crossing the Fermi level. This is in contrast to DFT plus dynamical mean field theory calculations, which reveal the Mott insulating behavior for the stoichiometric Pb$_{9}$Cu(PO$_4$)$_6$O compound. Nevertheless, the existing calculations are all based on the $P6_3/m$ structure, which is argued to be not the ground-state structure. Here, we revisit the electronic structure of Pb$_{9}$Cu(PO$_4$)$_6$O with the energetically more favorable $P\bar{3}$ structure, fully taking into account electronic symmetry breaking. We examine all possible configurations for Cu substituting the Pb sites. Our results show that the doped Cu atoms exhibit a preference for substituting the Pb2 sites than the Pb1 sites. In both cases, the calculated substitutional formation energies are large, indicating the difficulty in incorporating Cu at the Pb sites. We find that most of structures with Cu at the Pb2 site tend to be insulating, while the structures with both two Cu atoms at the Pb1 sites (except one configuration) are predicted to be metallic by DFT+$U$ calculations. However, when accounting for the electronic symmetry breaking, some Cu-doped configurations previously predicted to be metallic (including the structure studied in previous DFT+$U$ calculations) become insulating. Our work highlights the importance of symmetry breaking in obtaining correct electronic state for Pb$_{9}$Cu(PO$_4$)$_6$O, thereby reconciling previous DFT+$U$ and DFT+DMFT calculations.Comment: 19 pages, 9 figures (including Supplementary Material

Robust anomalous Hall effect in ferromagnetic metal under high pressure

Recently, the giant intrinsic anomalous Hall effect (AHE) has been observed in the materials with kagome lattice. In this study, we systematically investigate the influence of high pressure on the AHE in the ferromagnet LiMn6Sn6 with clean Mn kagome lattice. Our in-situ high-pressure Raman spectroscopy indicates that the crystal structure of LiMn6Sn6 maintains a hexagonal phase under high pressures up to 8.51 GPa. The anomalous Hall conductivity (AHC) {\sigma}xyA remains around 150 {\Omega}-1 cm-1, dominated by the intrinsic mechanism. Combined with theoretical calculations, our results indicate that the stable AHE under pressure in LiMn6Sn6 originates from the robust electronic and magnetic structure.Comment: 11 pages 5 figure

How to evaluate ex ante impact? An analysis of reviewers’ comments on impact statements in grant applications

Impact statements are increasingly required and assessed in grant applications. In this study, we used content analysis to examine the ‘comments on impact’ section of the postal reviews and related documents of Science Foundation Ireland’s Investigators’ Programme to understand reviewers’ ex ante impact assessment. We found three key patterns: (1) reviewers favoured short-term, tangible impacts, particularly commercial ones; (2) reviewers commented on process-oriented impact (formative) in a more concrete and elaborate manner than on outcome-oriented impact (summative); and (3) topics related to scientific impacts were widely discussed even though the impact section was to be used for evaluating economic and societal impacts. We conclude that for ex ante impact assessment to be effective, funding agencies should indicate the types of impact expected from research proposals clearly instead of a general ‘wish list’ and that more focus should be put on process-oriented impact than outcome-oriented impact.Science Foundation Irelan