As a consequence of their spin-orbit entangled ground state, many $5d^5$ iridate materials display a peculiar double-peak structure in optical transport quantities, such as absorption and conductivity. Their common interpretation is based on the presence of Hubbard subbands in the half-filled $j_{\mathrm{eff}}=1/2$ manifold. Herein, we challenge this picture, proposing a scenario based on the presence of spin-polaron (SP) quasiparticles, and assigning a dominant SP character to the first peak. We illustrate it by taking the materials ${\mathrm{Ba}}_2{\mathrm{IrO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ as paradigmatic examples, which we investigate within the dynamical mean-field theory and the self-consistent Born approximation. Both theories reproduce nontrivial features revealed by angle-resolved photoemission spectroscopy and optical transport measurements, supporting our interpretation. In the case of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ we show how the SP scenario survives in the low-doped regime. Similar optical transport fingerprints are expected to be found in the wider class of $5d^5$ iridates and more generally in strongly correlated antiferromagnetic regimes, such as those found in cuprates.

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• Optical conductivity
• Spin-orbit coupling
• Iridates
• Mott insulators
• Strongly correlated systems
• DFT+DMFT
• Dynamical mean field theory
• Materials modeling