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The spin-orbit Mott insulator Sr₂IrO₄ has raised tremendous interest recently due to striking similarities to high-T_c superconducting copper oxides both in the pure and in electron-doped compounds.
Here, we study the evolution of the spectral function of this 5d transition metal system as a function of doping by means of a combined ab-initio electronic structure and many-body quantum cluster approach. Thereby, important ingredients like spin-orbit coupling and distortions of the oxygen octahedra as well as Hubbard interactions and non-local charge fluctuations are taken into account. The spectral function of pure Sr₂IrO₄ is analyzed both in its high-temperature paramagnetic and in its low-temperature antiferromagnetic phase and the importance of non-local fluctuations is discussed. The spectra compare well with angular-resolved photoemission measurements and allow to study emerging changes under electron- and hole-doping. Special emphasis is placed on pseudogap features of the spectral function of electron-doped Sr₂IrO₄, which are found to be in good agreement with experiment.