Metal-insulator transition and enhanced superconducting pairing fluctuation in copper oxides induced by apex displacements*

In this work, we use a recently developed first principles method to explore how
displacement of the apical oxygen (A-O) in LCO affects the spin and charge
properties (charge and optical gap, susceptibilities, and superconducting order parameter).
We find, by combining QSGW and dynamical mean field theory (DMFT), that LCO is a Mott insulator;
but small displacements of the apical oxygens drive the compound to a metallic state through
a localizaiton/delocalization transition, with a concomitant maximum
$d$-wave order parameter at the transition.
We address the question whether NCO can be seen as the
limit of LCO with large apical displacements, and elucidate the deep
physical reasons why the behaviour of NCO is so different than the hole doped
materials. We shed new light on the recent correlation observed between T$_c$ and the
charge transfer gap \cite{gap_trend}, while also providing a guide towards the design of
optimized high-Tc superconductors. Further our results suggest that the strong correlation enough to induce Mott gap
may not be a prerequisite for high-Tc superconductivity.