Ly$\alpha$ Emitters with Very Large Ly$\alpha$ Equivalent Widths,
  EW$_{\rm 0}$(Ly$\alpha$) $\simeq 200-400$ \AA, at $z\sim 2$
  We present physical properties of spectroscopically confirmed Ly$\alpha$
emitters (LAEs) with very large rest-frame Ly$\alpha$ equivalent widths
EW$_{\rm 0}$(Ly$\alpha$). Although the definition of large EW$_{\rm
0}$(Ly$\alpha$) 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$\alpha$) $\simeq
200-400$ \AA\ given by careful continuum determinations with our deep
photometric and spectroscopic data. These large EW$_{\rm 0}$(Ly$\alpha$) 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 $L({\rm Ly\alpha})=3.7\times
10^{42}$ erg s$^{-1}$ and $M_{\rm UV}=-18.0$ as well as the blue UV continuum
slope of $\beta = -2.5\pm0.2$ and the low dust extinction $E(B-V)_{\rm *} =
0.02^{+0.04}_{-0.02}$, which indicate a high median Ly$\alpha$ escape fraction
of $f_{\rm esc}^{\rm Ly\alpha}=0.68\pm0.30$. This large $f_{\rm esc}^{\rm
Ly\alpha}$ value is explained by the low {\sc Hi} column density in the ISM
that is consistent with FWHM of the Ly$\alpha$ line, ${\rm FWHM
(Ly\alpha)}=212\pm32$ km s$^{-1}$, significantly narrower than those of small
EW$_{\rm 0}$(Ly$\alpha$) LAEs. Based on the stellar evolution models, our
observational constraints of the large EW$_{\rm 0}$ (Ly$\alpha$), the small
$\beta$, and the rest-frame He{\sc ii} equivalent width imply that at least a
half of our large EW$_{\rm 0}$(Ly$\alpha$) 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.
