Detectability of axion-like dark matter for different time-delay interferometry combinations in space-based gravitational wave detectors

In the space-based gravitational wave detections, the axion-like dark matter would alter the polarization state of the laser link between spacecrafts due to the birefringence effect. However, current designs of space-based laser interferometer are insensitive to variations in the polarization angle. Thus, the additional wave plates are employed to enable the response of the axion-induced birefringence effect. We calculate and compare the sensitivities of different space-based detectors, accounting for three time-delay interferometry combinations, including Monitor, Beacon, and Relay. We find that the Monitor and Beacon combinations have better sensitivity in the high-frequency range, and the optimal sensitivity reaches $g_{a\gamma}\sim 10^{-13}\text{GeV}^{-1}$, while the Sagnac combination is superior in the low-frequency range. We also find that ASTROD-GW can cover the detection range of axion-like dark matter mass down to $10^{-20}\text{eV}$.