  We present a statistical study of the planet-metallicity (P-M) correlation,
by comparing the 744 stars with candidate planets (SWPs) in the Kepler field
which have been observed with LAMOST, and a sample of distance-independent,
fake "twin" stars in the Kepler field with no planet reported (CKSNPs) yet.
With the well-defined and carefully-selected large samples, we find for the
first time a turn-off P-M correlation of Delta [Fe/H]_(SWPs-SNPs), which in
average increases from ~0.00+-0.03 dex to 0.06+-0.03 dex, and to 0.12+-0.03 for
stars with Earth, Neptune, Jupiter-sized planets successively, and then
declines to ~-0.01+-0.03 dex for more massive planets or brown dwarfs.
Moreover, the percentage of those systems with positive Delta[Fe/H] has the
same turn-off pattern. We also find FG-type stars follow this general trend,
but K-type stars are different. Moderate metal enhancement (~0.1-0.2 dex) for
K-type stars with planets of radii between 2 to 4 Earth radius as compared to
CKSNPs is observed, which indicates much higher metallicities are required for
Super-Earths, Neptune-sized planets to form around K-type stars. We point out
that the P-M correlation is actually metallicity-dependent, i.e., the
correlation is positive at solar and super-solar metallicities, and negative at
subsolar metallicities. No steady increase of Delta[Fe/H] against planet sizes
is observed for rocky planets, excluding the pollution scenario as a major
mechanism for the P-M correlation. All these clues suggest that giant planets
probably form differently from rocky planets or more massive planets/brown
dwarfs, and the core-accretion scenario is highly favoured, and high
metallicity is a prerequisite for massive planets to form.
