We improve the calculations of the elastic motion induced by dark matter hitting the surface of the mirror inside an interferometer used for gravitational-wave detection. We focus on the discovery potential of such a dark matter signal in the third-generation European gravitational-wave detector, the Einstein Telescope. By taking the thickness of the mirror into account, more than one resonance is predicted in the sensitive regime of the high-frequency interferometer. When the mass of dark matter is heavier than a few PeV or is highly boosted, the signal-to-noise ratio could exceed one, and the Einstein Telescope should be able to detect this dark matter signal.
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