  Particle dark matter could belong to a multiplet that includes an
electrically charged state. WIMP dark matter ($\chi^{0}$) accompanied by a
negatively charged excited state ($\chi^{-}$) with a small mass difference
(e.g. $<$ 20 MeV) can form a bound-state with a nucleus such as xenon. This
bound-state formation is rare and the released energy is $\mathcal{O}(1-10$)
MeV depending on the nucleus, making large liquid scintillator detectors
suitable for detection. We searched for bound-state formation events with xenon
in two experimental phases of the KamLAND-Zen experiment, a xenon-doped liquid
scintillator detector. No statistically significant events were observed. For a
benchmark parameter set of WIMP mass $m_{\chi^{0}} = 1$ TeV and mass difference
$\Delta m = 17$ MeV, we set the most stringent upper limits on the
recombination cross section times velocity $\langle\sigma v\rangle$ and the
decay-width of $\chi^{-}$ to $9.2 \times 10^{-30}$ ${\rm cm^3/s}$ and $8.7
\times 10^{-14}$ GeV, respectively at 90% confidence level.
