  In complex oxides, the electrons under the influence of competing energetics
are the cornerstone of coexistence (or phase-separation) of two or more
electronic/magnetic phases in same structural configuration. Probing of growth
and evolution of such phase-coexistence state is crucial to determine the
correct mechanism of related phase-transition. Here, we demonstrate the
combination of terahertz (THz) time-domain spectroscopy and DC transport as a
novel strategy to probe the electronic phase-coexistence. This is demonstrated
in disorder controlled phase-separated rare-earth nickelate thin films which
exhibit metal-insulator transition in dc conductivity at around 180 K but lack
this transition in terahertz (THz) dynamics conductivity down to low
temperature. Such pronounced disparity exploits two extreme attributes: i)
enormous sensitivity of THz radiation to a spatial range of its
wavelength-compatible electronic inhomogeneities and ii) insensitivity to a
range beyond the size of its wavelength. This feature is generic in nature
(sans a photo-induced effect), depends solely on the size of
insulating/metallic clusters and formulates a methodology with unique
sensitivity to investigate electronic phase-coexistence and phase transition of
any material system.
