  The supersymmetry (SUSY) breaking mechanism generally predicts the existence
of the sgoldstinos, which can play the role of wave-like dark matter. Due to
the ubiquitous coupling to the electromagnetic fields, the light scalar
sgoldstino dark matter can lead to the variance of the fine-structure constant.
With the precise atomic clock data, we find the SUSY breaking scale $\sqrt{F}$
can be probed up to the GUT scale in the sgoldstino mass range of $10^{-22}$ eV
$<m_\phi <$ $4\times10^{-7}$ eV.
