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We study the competition between various forms of density-wave-like orderparameters that may arise in multi-orbital correlated materials with strongspin-orbit coupling (SOC) within a renormalization-group (RG) approach. Thecalculations are restricted to models with two spin-orbit split bands havingstrong inter-band Fermi surface nesting. We find that for such Fermi surfacetopology, the interplay between the inter-band nesting and SOC stronglyenhances the inter-orbital Coulomb interaction (relative to other interactions)as the system approaches a stable fixed point. This results in an exoticspin-orbit density wave (SODW) to become the energetically favorablesymmetry-broken state. While the conclusions are generic to such a Fermisurface topology, the band structure and the numerical results are presentedfor the iridate systems. We also find that the electronic fingerprints of theSODW are in better agreement with various experimental results than aconventional spin density wave (SDW), explaining the long-standing problem ofthe origin of the metal-insulator transition in these systems.

A Renormalization-Group Study of the Symmetry-Breaking Order Parameters in Spin-Orbit Coupled Iridates and Related Systems