Charge order and superconductivity in a two-band model for infinite-layer nickelates

The recent discovery of superconductivity in infinite-layer nickelates has drawn considerable attention; however, a consensus on the fundamental building blocks and common ingredients is necessary to understand and describe their ground states and emergent properties is lacking. A series of experimental and theoretical studies have suggested that an effective two-band Hubbard model with Ni $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and rare-earth ($R$) $5d$ character may describe the low-energy physics. Here, we study the ground state properties of this two-band model on four-leg cylinders using the density-matrix renormalization group (DMRG) technique to better grasp whether such a simple model can embody the essential physics. A key difference compared to single-band Hubbard materials is that the system is self-doped: even at overall half-filling, the $R$ band acts as an electron reservoir, hole doping the Ni layer, and fundamentally altering the physics expected from an undoped antiferromagnet. On the four-leg cylinder, the ground state is consistent with a Luttinger liquid, with antiphase modulations of the charge density in the Ni and $R$ layers having corresponding wave vectors that lock together. Light hole doping away from half-filling releases the locking between the Ni and the $R$ charge modulations, as the electron density in the $R$ band decreases and eventually becomes exhausted at a hole doping concentration that depends sensitively on the effective splitting between the Ni and the $R$ orbitals. The ground state of the doped system is consistent with a Luther-Emery liquid, possessing quasi-long-range superconducting correlations in the Ni layer, similar to the single-band Hubbard model. Our results are consistent with experimental observations and may help to reveal the microscopic mechanism for pairing and other emergent properties not only in the infinite-layer nickelates but also other unconventional superconductors.