  A search for charged Higgs bosons decaying into a top quark and a bottom
quark is presented. The data analysed correspond to 139 fb$^{-1}$ of
proton-proton collisions at $\sqrt{s}$=13TeV, recorded with the ATLAS detector
at the LHC. The production of a heavy charged Higgs boson in association with a
top quark and a bottom quark, $pp\rightarrow tbH^{+}\rightarrow tbtb$, is
explored in the $H^+$ mass range from 200 to 2000 GeV using final states with
jets and one electron or muon. Events are categorised according to the
multiplicity of jets and $b$-tagged jets, and multivariate analysis techniques
are used to discriminate between signal and background events. No significant
excess above the background-only hypothesis is observed and exclusion limits
are derived for the production cross-section times branching ratio of a charged
Higgs boson as a function of its mass; they range from 3.6 pb at 200 GeV to
0.035 pb at 2000 GeV at 95% confidence level. The results are interpreted in
the hMSSM and $M_h^{125}$ scenarios.
