The Magellan M2FS Spectroscopic Survey of High-$z$ Galaxies: Ly{\alpha}
  Emitters at $z\approx6.6$ and the Evolution of Ly{\alpha} Luminosity Function
  over $z\approx5.7-6.6$
  We present a sample of Ly{\alpha} emitters (LAEs) at $z\approx6.6$ from our
spectroscopic survey of high-redshift galaxies using the multi-object
spectrograph M2FS on the Magellan Clay telescope. The sample consists of 36
LAEs selected by the narrow-band (NB921) technique over nearly 2 deg$^2$ in the
sky. These galaxies generally have high Ly{\alpha} luminosities spanning a
range of ${\sim}3\times10^{42}{-}7\times10^{43}$ erg s$^{-1}$, and include some
of the most Ly{\alpha}-luminous galaxies known at this redshift. They show a
positive correlation between the Ly{\alpha} line width and Ly{\alpha}
luminosity, similar to the relation previously found in $z\approx5.7$ LAEs.
Based on the spectroscopic sample, we calculate a sophisticated sample
completeness correction and derive the Ly{\alpha} luminosity function (LF) at
$z\approx6.6$. We detect a density bump at the bright end of the Ly{\alpha} LF
that is significantly above the best-fit Schechter function, suggesting that
very luminous galaxies tend to reside in overdense regions that have formed
large ionized bubbles around them. By comparing with the $z\approx5.7$
Ly{\alpha} LF, we confirm that there is a rapid LF evolution at the faint end,
but a lack of evolution at the bright end. The fraction of the neutral hydrogen
in the intergalactic medium at $z\approx6.6$ estimated from such a rapid
evolution is about $\sim0.3\pm0.1$, supporting a rapid and rather late process
of cosmic reionization.
