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√=8\ TeV 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~01) is the next-to-lightest supersymmetric particle and decays producing a Z boson and a gravitino ( G~) via the χ~01→ZG~ process.