This thesis describes a search for natural supersymmetry via the production of light top squarks (stops) with the ATLAS experiment, using 13 TeV proton-proton collision data delivered by the Large Hadron Collider. A range of models is considered where the stop may decay to top quarks, b jets, and a variety of other supersymmetric particles. Stop masses as large as 950 GeV are excluded at 95% confidence level when decaying to a top quark and massless lightest supersymmetric particle (LSP). In scenarios where the LSP is a Higgsino, exclusions vary from 600 to 900 GeV depending on the relative stop branching fractions and Higgsino mass splitting. The impact of precision top-quark measurements on future searches is also discussed, including a measurement of quantum interference in top-quark production and measurement of the top-quark width. A differential mass distribution is measured in events with two charged leptons and two b-tagged jets that is sensitive to the interference property. The measurement is unfolded to particle level and the data are compared to state-of-the-art Monte Carlo predictions, which are found to describe the data well. A new technique is proposed to utilize this dataset to extract a value of the top-quark width, inspired by recent efforts to measure the Higgs boson width using off-shell decays. A value of 1.28 ± 0.27(exp.)±0.15(theory) GeV is extracted from the ATLAS data, in good agreement with the standard model prediction. Finally, a new hardware tracking system is described for use in the upgraded ATLAS Trigger system for the high-luminosity run of the LHC.