  In the context of prospective studies for searches of new physics at the LHC
Run 3, this paper investigates the relevance of using top quarks produced from
new long-lived particles, and detected in the tracker volume of the ATLAS and
CMS experiments. Such a signature, referred to as displaced top quarks, leads
to final states containing displaced vertices and a high multiplicity of
displaced jets and tracks, thanks to the top quark decays. Therefore, it is a
possible powerful tool for searching for new long-lived particles. Three
simplified models based on supersymmetry are explicitly designed for the study
of this signature. They differ according to the nature of the long-lived heavy
particle which produces at least one top quark: electrically neutral or
charged, coloured or non-coloured long-lived particle. For each model, a wide
region of parameter space, consistent with a reasonable number of displaced top
quarks decaying in a typical tracker volume has been probed. From this study,
promising benchmarks are defined and experimental guidelines are suggested.
