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Ly$α$ Emitters with Very Large Ly$α$ Equivalent Widths, EW$_{\rm 0}$(Ly$α$) $\simeq 200-400$ Å, at $z\sim 2$

We present physical properties of spectroscopically confirmed Ly$α$ emitters (LAEs) with very large rest-frame Ly$α$ equivalent widths EW$_{\rm 0}$(Ly$α$). Although the definition of large EW$_{\rm 0}$(Ly$α$) LAEs is usually difficult due to limited statistical and systematic uncertainties, we identify six LAEs selected from $\sim 3000$ LAEs at $z\sim 2$ with reliable measurements of EW$_{\rm 0}$ (Ly$α$) $\simeq 200-400$ Å given by careful continuum determinations with our deep photometric and spectroscopic data. These large EW$_{\rm 0}$(Ly$α$) LAEs do not have signatures of AGN, but notably small stellar masses of $M_{\rm *} = 10^{7-8}$ $M_{\rm \odot}$ and high specific star-formation rates (star formation rate per unit galaxy stellar mass) of $\sim 100$ Gyr$^{-1}$. These LAEs are characterized by the median values of $L({\rm Lyα})=3.7\times 10^{42}$ erg s$^{-1}$ and $M_{\rm UV}=-18.0$ as well as the blue UV continuum slope of $β= -2.5\pm0.2$ and the low dust extinction $E(B-V)_{\rm *} = 0.02^{+0.04}_{-0.02}$, which indicate a high median Ly$α$ escape fraction of $f_{\rm esc}^{\rm Lyα}=0.68\pm0.30$. This large $f_{\rm esc}^{\rm Lyα}$ value is explained by the low {\sc Hi} column density in the ISM that is consistent with FWHM of the Ly$α$ line, ${\rm FWHM (Lyα)}=212\pm32$ km s$^{-1}$, significantly narrower than those of small EW$_{\rm 0}$(Ly$α$) LAEs. Based on the stellar evolution models, our observational constraints of the large EW$_{\rm 0}$ (Ly$α$), the small $β$, and the rest-frame He{\sc ii} equivalent width imply that at least a half of our large EW$_{\rm 0}$(Ly$α$) LAEs would have young stellar ages of $\lesssim 20$ Myr and very low metallicities of $Z<0.02 Z_\odot$ regardless of the star-formation history.