This thesis presents the results of a threefold research project: the construction of a phenomenological model for flavour changing (FC) interactions between top quarks and dark matter, the development of a new charm-jet tagging algorithm for the CMS experiment and finally an investigation of the potential use of that charm-tagging algorithm in a search for interactions, as predicted by this phenomenological model, in proton-proton collisions at the LHC. First an effective field theoretical description of this recently developed phenomenological model is presented in order to parametrise these interactions. Limits from dark matter relic abundances, direct and indirect dark matter searches are investigated and the calculated cross sections for possible processes at the LHC are discussed. In order to possibly improve the search for these flavour changing interactions, a new charm-tagging method is developed for the CMS experiment and its performance is optimised. Information from secondary vertices and displaced tracks in the hadronisation of charm quarks is combined with multivariate analysis techniques to identify jets from charm quarks and to distinguish them from light-flavour and gluon jets or from bottom jets. Finally an analysis is presented to identify proton-proton collision events at the LHC involving these FC top-quark dark matter interactions. This search is performed with a simple cut-based method and by applying template fitting. The new charm-tagging algorithm is shown to improve slightly the sensitivity of these searches with final-state charm jets.