  A search is made for potential $cc\bar{c}\bar{c}$ tetraquarks decaying into a
pair of charmonium states in the four muon final state using proton-proton
collision data at $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity
of 140 fb$^{-1}$ recorded by the ATLAS experiment at LHC. Two decay channels,
$J/\psi+J/\psi \rightarrow 4\mu$ and $J/\psi+\psi(2S) \rightarrow 4\mu$, are
studied. Backgrounds are estimated based on a hybrid approach involving Monte
Carlo simulations and data-driven methods. Statistically significant excesses
with respect to backgrounds dominated by the single parton scattering are seen
in the di-$J/\psi$ channel consistent with a narrow resonance at 6.9 GeV and a
broader structure at lower mass. A statistically significant excess is also
seen in the $J/\psi$+$\psi$(2S) channel. The fitted masses and decay widths of
the structures are reported.
