Probing compact dark matter with gravitational wave fringes detected by
  the Einstein Telescope
  Unlike the electromagnetic radiation from astrophysical objects,
gravitational waves (GWs) from binary star mergers have much longer wavelengths
and are coherent. For ground-based GW detectors, when the lens object between
the source and the earth has mass $\sim 1-10^5M_\odot$, the diffraction effect
should be considered since the chirping wavelengths are comparable to the scale
of the barrier (its Schwarzschild radius). The waveform will thus be distorted
as the fringes. In this work, we show that signals from the third-generation GW
detectors like the Einstein Telescope (ET) would be a smoking gun for probing
the nature of compact dark matter (CDM) or primordial black holes. Detection of
the lensing effects becomes harder when the lens mass is smaller. ET is more
sensitive than LIGO, the constraint is available for CDM mass $>5M_\odot$ while
LIGO can only detect the mass $>100M_\odot$. For a null search of the fringes,
one-year observation of ET can constrain the CDM density fraction to
$\sim10^{-2}-10^{-5}$ in the mass range $M_{\rm{CDM}}=10M_\odot-100M_\odot$.
