  Among the various candidates for dark matter (DM), ultralight vector DM can
be probed by laser interferometric gravitational wave detectors through the
measurement of oscillating length changes in the arm cavities. In this context,
KAGRA has a unique feature due to differing compositions of its mirrors,
enhancing the signal of vector DM in the length change in the auxiliary
channels. Here we present the result of a search for $U(1)_{B-L}$ gauge boson
DM using the KAGRA data from auxiliary length channels during the first joint
observation run together with GEO600. By applying our search pipeline, which
takes into account the stochastic nature of ultralight DM, upper bounds on the
coupling strength between the $U(1)_{B-L}$ gauge boson and ordinary matter are
obtained for a range of DM masses. While our constraints are less stringent
than those derived from previous experiments, this study demonstrates the
applicability of our method to the lower-mass vector DM search, which is made
difficult in this measurement by the short observation time compared to the
auto-correlation time scale of DM.
