Pulsar halos (also termed ‘TeV halo’) are a new class of γ-ray sources in Galaxy, which manifest as extended γ-ray emissions around middle-age pulsars, as discovered around the Gemigna pulsar, the Monogem pulsar and PSR J0622+3749 by HAWC and LHAASO. A consensus has been reached that the TeV emission comes from the inverse Compton scattering of escaping electrons from the PWN off soft background radiation field, while the particle transport mechanism in the halo is still in dispute. Currently, there are mainly three interpretations, namely, the isotropic, suppressed diffusion model, the isotropic, unsuppressed diffusion model with considering ballistic propagations of recently injected particles, and the anisotropic diffusion model. While the predicted gamma-ray surface brightness profiles by all three models can be more or less consistent with the observation, the implication of the three models for cosmic-ray transport mechanisms and the properties of interstellar magnetic field are quite different. In this study, we calculate the multiwavelength emission of pulsar halos expected by the three models. We show that the synchrotron radiation of these escaping electrons can produce a corresponding X-ray halo around the pulsar, and the expected surface brightness profiles are distinct in three models. We suggest sensitive X-ray detectors of a large FOV (such as eROSITA) with a reasonably long exposure time are crucial to understand the formation mechanisms of pulsar halos and serve as a probe to the properties of interstellar turbulence.