Correlated electronic structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Pb</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Cu</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>PO</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>6</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math>
Changming Yue, Viktor Christiansson, Philipp Werner
Abstract
Recently, above-room-temperature superconductivity was reported in the Cu-doped lead apatite ${\mathrm{Pb}}_{10\ensuremath{-}x}{\mathrm{Cu}}_{x}{({\mathrm{PO}}_{4})}_{6}\mathrm{O}$, dubbed LK-99. By relaxing the structure with Cu substitution, we derive a four-band low-energy model with two 3/4 filled bands of predominantly $\mathrm{Cu}\text{\ensuremath{-}}{d}_{xz,yz}$ character and two filled $\mathrm{O}\text{\ensuremath{-}}{p}_{x,y}$ bands. This model is further downfolded to a two-band $\mathrm{Cu}\text{\ensuremath{-}}{d}_{xz/yz}$ model. Using ab initio derived interaction parameters, we perform dynamical mean-field theory calculations to determine the correlated electronic structure in the normal state. These calculations yield a Mott insulator at $x=1$ and a strongly correlated non-Fermi-liquid metal upon doping. The very large interaction versus bandwidth ratio $U/W\ensuremath{\approx}30\ensuremath{-}50$ and the local moment paramagnetic behavior in the relevant filling regime are hard to reconcile with diamagnetism and high-temperature superconductivity. Our calculations suggest that this behavior comes from a component with a different stoichiometry.