Evolution of remnant Fermi surface state in lightly-doped correlated spin-orbit insulator Sr$_{2-x}$La$_x$IrO$_4$

Electronic structure has been studied in lightly electron doped correlated spin-orbit insulator Sr$_2$IrO$_4$ by angle-resolved photoelectron spectroscopy. We have observed coexistence of the lower Hubbard band and the in-gap band, the momentum dependence of the latter traces that of the band calculations without on-site Coulomb repulsion. The in-gap state remained anisotropically gapped in all observed momentum area, forming a remnant Fermi surface state, evolving towards the Fermi energy by carrier doping. These experimental results show a striking similarity with those observed in deeply underdoped cuprates, suggesting the common nature of the nodal liquid states observed in both compounds.