Unified mechanism of charge-density-wave and high-Tc superconductivity protected from oxygen vacancies in bilayer nickelates

Abstract Unconventional charge- and spin-density-wave states are commonly observed in bilayer nickelates, drawing considerable attention due to their proximity to high-transition temperature ( $${T}_{{\rm{c}}}$$ T c ) superconductivity. However, the nature and origin of these density waves remain poorly understood. Experiments show that the charge-density-wave and spin-density-wave transition temperatures are closely related but distinct, while mean-field-type analyses typically have yielded only a simple spin-density-wave phase. To resolve this key problem, this paper demonstrates that sizeable charge-density-wave instabilities emerge in proportion to spin-density-wave instabilities in La 3 Ni 2 O 7 due to the paramagnon-interference mechanism, which captures electron correlations beyond mean-field theories. Therefore, (i) the experimental charge- and spin-density-wave coexisting state is naturally explained, and (ii) charge- and spin-density-wave fluctuations cooperatively drive high- $${T}_{{\rm{c}}}$$ T c superconductivity. Furthermore, the predicted s-wave superconducting state is robust against the inner-apical oxygen vacancies. We find that the coexistence of charge- and spin-fluctuations is essential in bilayer nickelates, with both playing a cooperative role in mediating high- $${T}_{{\rm{c}}}$$ T c superconductivity.