Dual-phase xenon time projection chambers achieve optimal sensitivity for dark matter in the 10 to $1000{\mathrm{GeVc}}^{-2}$ mass range, but sub-GeV dark matter (DM) particles lack sufficient energy to produce nuclear recoils above detection thresholds in these detectors. Blazar-boosted dark matter offers a way to overcome this limitation. Relativistic jets in active galactic nuclei can accelerate light dark matter in their host-galaxy halos to energies that can leave detectable nuclear recoil signals in xenon-based detectors on Earth. We present the first blazar-boosted dark matter search that incorporates detector response modeling, using public data from XENON1T and LZ for the blazar TXS $0506+056$. We model dark matter-proton scattering in the jet environment, covering the full process from jet acceleration through to detector response. We explore how the host galaxy dark matter density profile impacts our analysis. We set model-dependent exclusion regions on the dark-matter–nucleon scattering cross section for $m_{\chi }\simeq 1\mathrm{MeV}{\text{c}}^{-2}$ dark matter, between $5.8\times {10}^{-31}{\mathrm{cm}}^2$ and $6.3\times {10}^{-29}{\mathrm{cm}}^2$ using XENON1T data, and between $9.9\times {10}^{-32}{\mathrm{cm}}^2$ and $2.5\times {10}^{-28}{\mathrm{cm}}^2$ from LZ effective field theory dark matter searches. Our results show that astrophysical uncertainties, especially those in the dark-matter distribution near the supermassive black hole, are the main limitation of this search rather than detector effects. The limits are therefore model-dependent and should be seen as exploratory. They highlight both the potential and the present uncertainties of blazar-boosted dark matter as a probe of light dark matter.

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