Hole distribution and self-doping enhanced electronic correlation in hole-doped infinite-layer nickelates

The minimal model for infinite-layer nickelates remains under debate, particularly regarding the hybridization between itinerant interstitial-$s$ and the correlated Ni-3$d_{x^2-y^2}$ orbitals, as well as the interaction between $d_{x^2-y^2}$ and other $3d$ orbitals. Additionally, how the doped holes in La$_{1-x}$Sr$_x$NiO$_2$ are distributed among different orbitals remain unresolved. Motivated by recent angle resolved photoemission spectroscopy (ARPES) experiments, we theoretically study the electronic structure of infinite-layer La$_{1-x}$Sr$_x$NiO$_2$ at various doping levels. We find that, unlike the expectation from a rigid band shift, holes are equally distributed to Ni-3$d_{x^2-y^2}$ and interstitial-$s$ orbitals. The role of interstitial-$s$ orbital is further confirmed from the renormalization of Ni-3$d_{x^2-y^2}$ band, for which the coupling between interstitial-$s$ and Ni-3$d_{x^2-y^2}$ exerts a non-negligible impact on the orbital-selective renormalization observed in ARPES. We also discuss the implication of our results to the single-band model, where the interstitial-$s$ orbital in the normal state of La$_{1-x}$Sr$_x$NiO$_2$ acts as charge donator enhancing the correlation of Ni-3$d_{x^2-y^2}$ by increasing its concentration close to half-filling.