Origin of Flat Bands and Role of Electron Correlation in Lutetium Hydrides

Abstract

Lutetium hydrides (LuH$_x$, $1.75 \leq x \leq 3$) form a diverse series of phases, several of which superconduct under pressure. Characterizing their electronic properties has remained challenging owing to a high propensity for hydrogen defect formation, and recent angle-resolved photoemission (ARPES) measurements reveal puzzling flat-band regions that position these materials as candidates where superconductivity and flat-band physics may intersect. Here, by combining density functional theory, dynamical mean-field theory, and the constrained random-phase approximation, we uncover the microscopic origin and correlation nature of these flat bands. Across all compositions, the screened on-site Coulomb interaction is larger for H-s states than for Lu-$d$ states due to compact hydrogen orbitals. Nevertheless, these systems remain weakly correlated metals: the nearly filled H-$s$ shell admits little charge fluctuation, so its large interaction acts as a static level shift rather than a source of correlation. Although hydrogen primarily occupies tetrahedral sites at $x=2$, we discover that anti-site defects--where hydrogens occupy slightly unfavorable octahedral sites--generate both the ARPES flat-band features and the low-energy optical absorption peak, attesting to the usual defective nature of such materials in experimental samples. We further find that correlation strength is governed primarily by hydrogen orbital filling at these sites rather than the interaction magnitude itself. Consequently, we identify hydrogen orbital filling as the fundamental organizing principle dictating correlation and low-energy flat-band physics in lutetium hydrides.