Search for a CP-odd Higgs boson decaying to a heavy CP-even Higgs boson and a $Z$ boson in the $\ell\ell t\bar{t}$ and $\nu\bar{\nu}b\bar{b}$ final states using 140 fb$^{-1}$ of data collected with the ATLAS detector

A search for a heavy $CP$-odd Higgs boson, $A$, decaying into a $Z$ boson and a heavy $CP$-even Higgs boson, $H$, in the $\ell\ell t\bar{t}$ and $\nu\bar{\nu}b\bar{b}$ final states is presented using the full LHC Run 2 dataset of $pp$ collisions collected with the ATLAS detector at $\sqrt{s}=13$ TeV and corresponding to an integrated luminosity of $140$~fb$^{-1}$. The search for $A\to ZH$ is performed for the first time in the $\ell\ell t\bar{t}$ and $\nu\bar{\nu}b\bar{b}$ final states and extends the reach of previous searches in different final states in the region with $m_H>350$ GeV and $m_A>800$ GeV. No significant deviations from the Standard Model expectation are found and therefore upper limits on the production cross-section times the decay branching ratios are set. An interpretation of the results in the context of two-Higgs-doublet models is also given.