Single top and rare top quark production (including FCNC searches) at ATLAS and CMS

Measurements of single top and rare top quark production may be sensitive to theories of physics beyond the standard model (SM), including those in which the energy scale of new physics is beyond the energies directly accessible at the Large Hadron Collider. Such models may be observable through signatures like forbidden SM interactions or deviations of the top quark's couplings from the SM predictions. An overview of recent searches from the ATLAS and CMS Collaborations is presented, with a focus on flavor-changing neutral currents.