Electron Glass Phase with Resilient Zhang-Rice Singlets in LiCu3O3

${\text{LiCu}}_{3}{\mathrm{O}}_{3}$ is an antiferromagnetic mixed valence cuprate where trilayers of edge-sharing Cu(II)O ($3{d}^{9}$) are sandwiched in between planes of Cu(I) ($3{d}^{10}$) ions, with Li stochastically substituting Cu(II). Angle-resolved photoemission spectroscopy (ARPES) and density functional theory reveal two insulating electronic subsystems that are segregated in spite of sharing common oxygen atoms: a Cu ${d}_{{z}^{2}}/\mathrm{O}$ ${p}_{z}$ derived valence band (VB) dispersing on the Cu(I) plane, and a Cu $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}/\mathrm{O}$ $2{p}_{x,y}$ derived Zhang-Rice singlet (ZRS) band dispersing on the Cu(II)O planes. First-principle analysis shows the Li substitution to stabilize the insulating ground state, but only if antiferromagnetic correlations are present. Li further induces substitutional disorder and a 2D electron glass behavior in charge transport, reflected in a large 530 meV Coulomb gap and a linear suppression of VB spectral weight at ${E}_{F}$ that is observed by ARPES. Surprisingly, the disorder leaves the Cu(II)-derived ZRS largely unaffected. This indicates a local segregation of Li and Cu atoms onto the two separate corner-sharing $\mathrm{Cu}(\mathrm{II}){\mathrm{O}}_{2}$ sub-lattices of the edge-sharing Cu(II)O planes, and highlights the ubiquitous resilience of the entangled two hole ZRS entity against impurity scattering.