In-gap states and strain-tuned band convergence in layered structure trivalent iridate K_0.75Na_0.25IrO₂

Iridium oxides (iridates) provide a good platform to study the delicate interplay between spin-orbit coupling (SOC) interactions, electron correlation effects, Hund's coupling and lattice degrees of freedom. An overwhelming number of investigations primarily focus on tetravalent (Ir⁴⁺, 5d⁵) and pentavalent (Ir⁵⁺, 5d⁴) iridates, and far less attention has been paid to iridates with other valence states. Here, we pay our attention to a less-explored trivalent (Ir³⁺, 5d⁶) iridate, K_0.75Na_0.25IrO₂, crystallizing in a triangular lattice with edge-sharing IrO₆ octahedra and alkali metal ion intercalated [IrO₂]^- layers, offering a good platform to explore the interplay between different degrees of freedom. We theoretically determine the preferred occupied positions of the alkali metal ions from energetic viewpoints and reproduce the experimentally observed semiconducting behavior and nonmagnetic (NM) properties of K_0.75Na_0.25IrO₂. The SOC interactions play a critical role in the band dispersion, resulting in NM J_eff = 0 states. More intriguingly, our electronic structure not only uncovers the presence of intrinsic in-gap states and nearly free electron character for the conduction band minimum, but also explains the abnormally low activation energy in K_0.75Na_0.25IrO₂. Particularly, the band edge can be effectively modulated by mechanical strain, and the in-gap states feature enhanced band-convergence characteristics by 6% compressive strain, which will greatly enhance the electrical conductivity of K_0.75Na_0.25IrO₂. The present work sheds new light on the unconventional electronic structures of trivalent iridates, indicating their promising application as a nanoelectronic and thermoelectric material, which will attract extensive interest and stimulate experimental works to further understand the unprecedented electronic structures and exploit potential applications of the triangular trivalent iridate.