A search for ultra-high energy photons with energies above 1 EeV is performed using nine years of data collected by the Pierre Auger Observatory in hybrid operation mode. An unprecedented separation power between photon and hadron primaries is achieved by combining measurements of the longitudinal air-shower development with the particle content at ground measured by the fluorescence and surface detectors, respectively. Only three photon candidates at energies 1 - 2 EeV are found, which is compatible with the expected hadron-induced background. Upper limits on the integral flux of ultra-high energy photons of 0.038, 0.010, 0.009, 0.008 and 0.007 km$^{-2}$ sr$^{-1}$ yr$^{-1}$ are derived at 95% C.L. for energy thresholds of 1, 2, 3, 5 and 10 EeV. These limits bound the fractions of photons in the all-particle integral flux below 0.14%, 0.17%, 0.42%, 0.86% and 2.9%. For the first time the photon fraction at EeV energies is constrained at the sub-percent level. The improved limits are below the flux of diffuse photons predicted by some astrophysical scenarios for cosmogenic photon production. The new results rule-out the early top-down models $-$ in which ultra-high energy cosmic rays are produced by, e.g., the decay of super-massive particles $-$ and challenge the most recent super-heavy dark matter models.
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