Ly$alpha$ Emitters (LAEs) may represent an important galaxy population in the low mass regime. We present our deep narrowband imaging surveys in the COSMOS and ECDF-S fields and study the properties of LAEs at $z=2.23pm0.03$. The narrowband surveys conducted at Magellan II telescope allow us to obtain a sample of 452 LAEs reaching a $5sigma$ limiting magnitude of $sim26$ mag. Our Ly$alpha$ luminosity functions extend to $10^{41.8}$ erg s$^{-1}$ with steep faint-end slope. Using multi-wavelength ancillary data, especially the deep Spitzer/IRAC 3.6$mu$m and 4.5$mu$m photometric data, we obtained reliable stellar mass estimates for 130 IRAC-detected LAEs, spanning a range of $8 < {rm log}(M_star/M_odot)< 11.5$. For the remaining IRAC-undetected LAEs, the median-stacked spectral energy distribution yields a stellar mass of ${rm log}(M_star/M_odot)=7.97^{+0.05}_{-0.07}$ and the rest-frame ultraviolet emission indicates a median star formation rate of ${rm log} (SFR/M_odot$ yr$^{-1})=-0.14pm0.35$. There are six LAEs detected by the Spitzer/MIPS 24$mu$m or even Herschel far-infrared observations. Taking into account the six MIR/FIR detected LAEs, our LAEs cover a wide range in the star formation rate (${rm 1<SFR<2000}$ M$_odot$ yr$^{-1}$). Although LAEs as a population are diverse in their stellar properties, they are mostly low-mass star-forming galaxies and follow the star formation main sequence relations or their extrapolations to the low-mass end, implying a normal star-forming nature of LAEs. The clustering analysis indicates that our LAEs reside in dark matter halos with ${rm <log(M_{h}/M_{odot})> =10.8^{+0.56}_{-1.1}}$, suggesting that they are progenitors of local Large Magellanic Cloud-like galaxies.
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