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Structural phase separation in the form of partially disordered stripes, withcharacteristic length scales in the nanometer range, is observed forsuperconducting BaPb$_{1-x}$Bi$_x$O$_3$. The evolution of the superconductingcoherence length with composition relative to the size of these stripessuggests an important role of the nanostructure in determining the shape of thesuperconducting dome. It is proposed that the maximum $T_c$ is determined by akind of "optimal inhomogeneity", characterized by a crossover from aninhomogeneous macroscopic superconductor to a granular superconductor for whichphase fluctuations suppress $T_c$.

Stripe-like nanoscale structural phase separation and optimal inhomogeneity in superconducting BaPb$_{1-x}$Bi$_x$O$_3$