  It is widely believed that high-temperature superconductivity in the cuprates
emerges from doped Mott insulators. The physics of the parent state seems
deceivingly simple: The hopping of the electrons from site to site is
prohibited because their on-site Coulomb repulsion U is larger than the kinetic
energy gain t. When doping these materials by inserting a small percentage of
extra carriers, the electrons become mobile but the strong correlations from
the Mott state are thought to survive; inhomogeneous electronic order, a
mysterious pseudogap and, eventually, superconductivity appear. How the
insertion of dopant atoms drives this evolution is not known, nor whether these
phenomena are mere distractions specific to hole-doped cuprates or represent
the genuine physics of doped Mott insulators. Here, we visualize the evolution
of the electronic states of (Sr1-xLax)2IrO4, which is an effective spin-1/2
Mott insulator like the cuprates, but is chemically radically different. Using
spectroscopic-imaging STM, we find that for doping concentration of x=5%, an
inhomogeneous, phase separated state emerges, with the nucleation of pseudogap
puddles around clusters of dopant atoms. Within these puddles, we observe the
same glassy electronic order that is so iconic for the underdoped cuprates.
Further, we illuminate the genesis of this state using the unique possibility
to localize dopant atoms on topographs in these samples. At low doping, we find
evidence for much deeper trapping of carriers compared to the cuprates. This
leads to fully gapped spectra with the chemical potential at mid-gap, which
abruptly collapse at a threshold of around 4%. Our results clarify the melting
of the Mott state, and establish phase separation and electronic order as
generic features of doped Mott insulators.
