Observation of $e^+e^-\to \pi^0\pi^0 h_c$ and a neutral charmoniumlike structure $Z_c(4020)^0$

Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider at center-of-mass energies of $\sqrt{s}=4.23$, 4.26, and 4.36~GeV, we observe $\EE\to \pphc$ for the first time. The Born cross sections are measured and found to be about half of those of $\EE\to \pi^+\pi^-h_c$ within less than 2$\sigma$. In the $\pi^0h_c$ mass spectrum, a structure at 4.02~GeV/$c^2$ is found. It is most likely to be the neutral isospin partner of the $\zcp^{\pm}$ observed in the process of $\EE\to \pi^+\pi^-h_c$ is found. A fit to the $\pi^0 h_c$ invariant mass spectrum, with the width of the $\zcpn$ fixed to that of its charged isospin partner and possible interferences with non-$\zcpn$ amplitudes neglected, gives a mass of ($4023.9\pm 2.2 \pm 3.8$)~MeV/$c^2$ for the $\zcpn$, where the first error is statistical and the second systematic.