Anomalous couplings in single top quark and searches for rare top quark couplings with the ATLAS detector

Two recent analyses that have exhaustively explored potential anomalous couplings in the $Wtb$ vertex using $t$-channel single-top-quark events selected from collision data at $\sqrt{s} = $ 8 TeV with the ATLAS detector are reviewed. The first one measures the top-quark polarisation and six W-boson spin opservables from angular asymmetries unfolded to parton level. The second one measures the normalised triple-differential angular decay rate of top quarks to simultaneously constrain all the anomalous couplings. The limits on the anomalous couplings improve the existing limits set by ATLAS at $\sqrt{s} = $ 7 TeV. In addition, searches for flavour-changing neutral current top-quark interactions based on data collected by ATLAS and CMS, are reviewed. Finally, a recent search for $t \rightarrow qH$, with $H \rightarrow \gamma\gamma$, performed by ATLAS at $\sqrt{s} = $ 13 TeV is also presented, where previous LHC limits are improved.