Exploring Reionization-Era Quasars III: Discovery of 16 Quasars at
  $6.4\lesssim z \lesssim 6.9$ with DESI Legacy Imaging Surveys and UKIRT
  Hemisphere Survey and Quasar Luminosity Function at $z\sim6.7$
  This is the third paper in a series aims at finding reionzation-era quasars
with the combination of DESI Legacy imaging Surveys (DELS) and near-infrared
imaging surveys, such as the UKIRT Hemisphere Survey (UHS), as well as the
Wide-field Infrared Survey Explore ($WISE$) mid-infrared survey. In this paper,
we describe the updated quasar candidate selection procedure, report the
discovery of 16 quasars at $6.4\lesssim z \lesssim6.9$ from area of
$\sim$13,020 deg$^2$, and present the quasar luminosity function (QLF) at
$z\sim6.7$. The measured QLF follows $\Phi(L_{1450})\propto L_{1450}^{-2.35}$
in the magnitude range $27.6<M_{1450}<-25.5$. We determine the quasar comoving
spatial density at $\langle z \rangle$=6.7 and $M_{1450}<-26.0$ to be $\rm
0.39\pm0.11 Gpc^{-3}$ and find that the exponential density evolution parameter
to be $k=-0.78\pm0.18$ from $z\sim6$ to $z\sim6.7$, corresponding to a rapid
decline by a factor of $\sim 6$ per unit redshift towards earlier epoch, a rate
significantly faster than that at $z\sim 3- 5$. The cosmic time between
$z\sim6$ and $z\sim6.7$ is only 121 Myrs. The quasar density declined by a
factor of more than three within such short time requires that SMBHs must grow
rapidly or they are less radiatively efficient at higher redshifts. We measured
quasar comoving emissivity at $z\sim6.7$ which indicate that high redshift
quasars are highly unlikely to make a significant contribution to hydrogen
reionization. The broad absorption line (BAL) quasar fraction at $z\gtrsim6.5$
is measured to be $\gtrsim$22%. In addition, we also report the discovery of
additional five quasars at $z\sim6$ in the appendix.
