Extremely low-mass galaxies at high redshifts may be at a very early evolutionary stage before settling into the star-formation main sequence (SFMS). Around cosmic noon, while galaxies down to stellar masses Ms~10^8 Msun have been studied well with identification of the SFMS (Popping et al. 2015), only less than 30 galaxies (at z~2-2.5) have been found below this mass limit (e.g., Hagen et al. 2015) and they have no halo-mass estimates needed for discussion in the cosmological context. We select ~300 galaxies with Ms <10^8 Msun from our large z=2.2 Lyα emitter sample in the SXDS field, by using UV properties. They have faint UV magnitudes > -19.1 mag, blue UV slopes < -1.9, or bright Lyα luminosities >~ 4.5×10^41 erg/s. We find that they are star-burst galaxies with star formation rates (SFRs) of ~10 Msun/yr by SED fitting of stacked spectra. Their dark matter halo masses are estimated to be <~ 10^11 Msun by clustering analysis. The following results imply that these extremely low-mass galaxies would be in a short-time star-burst phase (possibly before supernova feedback occurs) and may fall down towards the SFMS immediately: 1) their baryon conversion efficiencies (SFR divided by baryon accretion rate) probably reach ~ 1, being higher than the expectation in the case of MS galaxies (Behroozi et al. 2013), 2) their stellar to halo mass ratios are possibly comparable with those of MS galaxies, 3) they have young ages <~ 10 Myr, and 4) their number density is much lower than a low-mass extrapolation of the stellar mass function (Tomczak et al. 2014). We will discuss the mechanisms enabling their very high star-formation activities. We will also discuss the amount of Ly continuum photons escaping from these galaxies as low-z analogs of ionizing sources at the epoch of reionization.