This note presents direct searches for lepton flavour violation in Higgs boson decays, $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, performed with the ATLAS detector at the LHC. The searches are based on a data sample of $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 36.1\,\text{fb}^{-1}. No significant excesses over the SM predictions are observed and upper limits on the lepton-flavour-violating branching ratios are set. The observed (median expected) 95\% confidence level upper limits are 0.47% ($0.34^{+0.13}_{-0.10}$ %) and 0.28% ($0.37^{+0.14}_{-0.10}$ %) for $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, respectively.

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