A search is presented for direct top squark pair production using events with at least two leptons including a same-flavour opposite-sign pair with invariant mass consistent with the Z boson mass, jets tagged as originating from b -quarks and missing transverse momentum. The analysis is performed with proton–proton collision data at s=8TeV collected with the ATLAS detector at the LHC in 2012 corresponding to an integrated luminosity of 20.3 fb -1 . No excess beyond the Standard Model expectation is observed. Interpretations of the results are provided in models based on the direct pair production of the heavier top squark state ( t~2 ) followed by the decay to the lighter top squark state ( t~1 ) via t~2→Zt~1 , and for t~1 pair production in natural gauge-mediated supersymmetry breaking scenarios where the neutralino ( χ~10 ) is the next-to-lightest supersymmetric particle and decays producing a Z boson and a gravitino ( G~ ) via the χ~10→ZG~ process.