Discovery strategies for dark matter and Higgsinos at the LHC

New dynamics beyond the Standard Model is expected at scales probed by the Large Hadron Collider. In particular, weak scale supersymmetry can provide a dark matter candidate and stabilise the electroweak hierarchy. This thesis presents two studies investigating new strategies to discover such phenomena. First, a theoretical assessment uses six search strategies based on 3.2 fb$^{-1}$ of 13 TeV data to constrain a 19-parameter framework of supersymmetry. This identified the fermionic partners of Higgs bosons, called Higgsinos, as a key target for dark matter searches. Such scenarios are very difficult to discover at colliders in electroweak production, as produced states are one to tens of GeV heavier than the dark matter and leave little detector activity. The second part of this thesis presents a new experimental strategy targeting these so-called compressed scenarios, exploiting electrons and muons down to the lowest transverse momenta detectable by the ATLAS Experiment. Using 36.1 fb$^{-1}$ of 13 TeV data, this strategy opens hadron collider sensitivity to Higgsino dark matter down to mass splittings of 3 GeV, and coannihilation scenarios involving winos and sleptons down to mass splittings of 2.5 and 1 GeV respectively. While no statistically significant excesses are observed, this landmark LHC sensitivity surpasses lepton collider limits for the first time in nearly two decades.