The role of correlations in the low energy electronic structure of ligthly electron doped Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$.

We characterized the emergence of exotic electronic ground states in lightly electron doped (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ and (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ by ARPES. In the single layer iridate, a large Fermi surface with nodal coherent spectral weight and antinodal pseudogap emerges, concomitantly with the collapse of the Mott gap, upon doping [1]. On the other hand, in Sr$_3$Ir$_2$O$_7$ a small non-gapped Fermi surface with coherent quasiparticles, together with a reduction of the correlated gap throughout the entire Brillouin Zone is observed when doping above the insulator to metal transition [2]. By comparing the electronic structure of these two materials, we provide evidence that the interplay between spin-orbit and electron-electron correlations ($U$) in (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ and (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ is rather different: while in Sr$_2$IrO$_4$ this interplay results in a pseudospin-1/2 single band Mott insulator with a phenomenology very similar to that of cuprates, in Sr$_3$Ir$_2$O$_7$ $U$ enhances the bilayer splitting gap to originate a ground state resembling that of a correlated semiconductor. [1] A. de la Torre et al, PRL 115, 176402 (2015); [2] A. de la Torre et al, PRL 113, 256402 (2014)