Discovery of a very Lyman-$\alpha$-luminous quasar at z=6.62
  Distant luminous quasars provide important information on the growth of the
first supermassive black holes, their host galaxies and the epoch of
reionization. The identification of quasars is usually performed through
detection of their Lyman-$\alpha$ line redshifted to $\sim$ 0.9 microns at
z>6.5. Here, we report the discovery of a very Lyman-$\alpha$ luminous quasar,
PSO J006.1240+39.2219 at redshift z=6.618, selected based on its red colour and
multi-epoch detection of the Lyman-$\alpha$ emission in a single near-infrared
band. The Lyman-$\alpha$-line luminosity of PSO J006.1240+39.2219 is unusually
high and estimated to be 0.8$\times$10$^{12}$ Solar luminosities (about 3% of
the total quasar luminosity). The Lyman-$\alpha$ emission of PSO
J006.1240+39.2219 shows fast variability on timescales of days in the quasar
rest frame, which has never been detected in any of the known high-redshift
quasars. The high luminosity of the Lyman-$\alpha$ line, its narrow width and
fast variability resemble properties of local Narrow-Line Seyfert 1 galaxies
which suggests that the quasar is likely at the active phase of the black hole
growth accreting close or even beyond the Eddington limit.
