  We present a search for dark photon dark matter that could couple to
gravitational-wave interferometers using data from Advanced LIGO and Virgo's
third observing run. To perform this analysis, we use two methods, one based on
cross-correlation of the strain channels in the two nearly aligned LIGO
detectors, and one that looks for excess power in the strain channels of the
LIGO and Virgo detectors. The excess power method optimizes the Fourier
Transform coherence time as a function of frequency, to account for the
expected signal width due to Doppler modulations. We do not find any evidence
of dark photon dark matter with a mass between $m_{\rm A} \sim
10^{-14}-10^{-11}$ eV/$c^2$, which corresponds to frequencies between 10-2000
Hz, and therefore provide upper limits on the square of the minimum coupling of
dark photons to baryons, i.e. $U(1)_{\rm B}$ dark matter. For the
cross-correlation method, the best median constraint on the squared coupling is
$\sim2.65\times10^{-46}$ at $m_{\rm A}\sim4.31\times10^{-13}$ eV/$c^2$; for the
other analysis, the best constraint is $\sim 2.4\times 10^{-47}$ at $m_{\rm
A}\sim 5.7\times 10^{-13}$ eV/$c^2$. These limits improve upon those obtained
in direct dark matter detection experiments by a factor of $\sim100$ for
$m_{\rm A}\sim [2-4]\times 10^{-13}$ eV/$c^2$, and are, in absolute terms, the
most stringent constraint so far in a large mass range $m_A\sim$ $2\times
10^{-13}-8\times 10^{-12}$ eV/$c^2$.
