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Many complex electronic systems exhibit so-called pseudogaps, which arepoorly-understood suppression of low-energy spectral intensity in the absenceof an obvious gap-inducing symmetry. Here we investigate the superconductor$Ba_{1-x}K_{x}BiO_{3}$ near optimal doping, where unconventional transportbehavior and evidence of pseudogap(s) have been observed above thesuperconducting transition temperature $T_{c}$, and near an insulating phasewith long-range lattice distortions. Angle-resolved photoemission spectroscopy(ARPES) reveals a dispersive band with vanishing quasiparticle weight and"tails" of deep-energy intensity that strongly decay approaching the Fermilevel. Upon cooling below a transition temperature $T_{p} > T_{c}$, whichcorrelates with a change in the slope of the resistivity vs. temperature, apartial transfer of spectral weight near $E_{F}$ into the deep-binding energytails is found to result from metal-insulator phase separation. Combined withsimulations and Raman scattering, our results signal that insulating islands ofordered bipolarons precipitate out of a disordered polaronic liquid and provideevidence that this process is regulated by a crossover in the electronic meanfree path.

Cooling a polaronic liquid: Phase mixture and pseudogap-like spectra in superconducting $Ba_{1-x}K_{x}BiO_{3}$