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We present a promising application of epsilon-near-zero (ENZ) materials in optical modulators. When a thin ENZ film is sandwiched in a single-mode waveguide, an ENZ-slot waveguide is formed, where the absorption can be greatly enhanced. We propose electroabsorption modulators based on tunable ENZ materials and slot waveguides. Transparent conducting oxides (TCOs) may be employed as the active slot, which can be tuned between ENZ (high absorption) and epsilon-far-from-zero (low absorption) by accumulation carriers. Numerical simulation shows that over 3-dB modulation depth can be achieved in a 250-nm-long TCO-slot waveguide. The modulators have the advantages of nanoscale footprints, small insertion loss, potentially ultrahigh speed, and easy fabrication.