Nonlocal Coulomb correlations in pure and electron-doped Sr2IrO4: Spectral functions, Fermi surface, and pseudo-gap-like spectral weight distributions from oriented cluster dynamical mean-field theory

We address the role of nonlocal Coulomb correlations and short-range magnetic fluctuations in the high-temperature phase of ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ within state-of-the-art spectroscopic and first-principles theoretical methods. Introducing an ``oriented-cluster dynamical mean-field scheme'', we compute momentum-resolved spectral functions, which we find to be in excellent agreement with angle-resolved photoemission spectra. We show that while short-range antiferromagnetic fluctuations are crucial to accounting for the electronic properties of ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ even in the high-temperature paramagnetic phase, long-range magnetic order is not a necessary ingredient of the insulating state. Upon doping, an exotic metallic state is generated, exhibiting cuprate-like pseudo-gap spectral properties, for which we propose a surprisingly simple theoretical mechanism.