Coherent and incoherent bands in La and Rh doped Sr$_3$ Ir$_2$ O$_7$

International audience; In Sr$_2$ IrO$_4$ and Sr$_3$ Ir$_2$ O$_7$ , correlations, magnetism, and spin-orbit coupling compete on similar energy scales, creating a new context to study metal-insulator transitions (MIT). We use here angle-resolved photoemission to investigate the MIT as a function of hole and electron doping in Sr$_3$ Ir$_2$ O$_7$ , obtained respectively by Ir/Rh and Sr/La substitutions. We show that there is a clear reduction as a function of doping of the gap between a lower and upper band on both sides of the Fermi level, from 0.2 to 0.05 eV. Although these two bands have a counterpart in band structure calculations, they are characterized by a very different degree of coherence. The upper band exhibits clear quasiparticle peaks, while the lower band is very broad and loses weight as a function of doping. Moreover, their ARPES spectral weights obey different periodicities, reinforcing the idea of their different nature. We argue that a very similar situation occurs in Sr$_2$ IrO$_4$ and conclude that the physics of the two families is essentially the same.