High-harmonic generation (HHG) has been used to generate extreme ultra-violet (EUV) light sources to probe fast electron dynamics in the attosecond time scale. While traditionally observed in rare-gas atoms, HHG has also recently been reported in solids, with reduced threshold pump field and the additional advantage of producing stable EUV waveforms in a compact setup. Unfortunately, above-band-gap absorption restricts the HHG process to a very thin layer of the solid-state material (typically tens of nanometers in thickness), significantly limiting the generation efficiency. Here, we use a material operating in its epsilon-near-zero (ENZ) region, where the real part of its permittivity vanishes, to greatly boost the efficiency of the HHG process at the microscopic level. In experiments, we report high-harmonic emission up to the 9th order directly from a low-loss, solid-state ENZ medium: indium-doped cadmium oxide, with an excitation intensity at the GW cm-2 level. Furthermore, the observed HHG signal exhibits a pronounced spectral red-shift as well as linewidth broadening, resulting from the photo-induced electron heating and the consequent time-dependent resonant frequency of the ENZ film. Our results provide a novel nanophotonic platform for strong field physics, reveal new degrees of freedom for spectral and temporal control of HHG, and open up possibilities of compact solid-state attosecond light sources
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