The host star metallicity provide a measure of the conditions in protoplanetary disks at the time of planet formation .
Using a sample of over 20,000 Kepler stars with spectroscopic metallicities from the LAMOST survey , we explore how the exoplanet population depends on host star metallicity as a function of orbital period and planet size .
We find that exoplanets with orbital periods less than 10 days are preferentially found around metal-rich stars ( [ Fe/H ] \simeq { } 0.15 \pm 0.05 dex ) .
The occurrence rates of these hot exoplanets increases to \sim { } 30 \% for super-solar metallicity stars from \sim { } 10 \% for stars with a sub-solar metallicity .
Cooler exoplanets , that reside at longer orbital periods and constitute the bulk of the exoplanet population with an occurrence rate of \gtrsim { } 90 \% , have host-star metallicities consistent with solar .
At short orbital periods , P < 10 days , the difference in host star metallicity is largest for hot rocky planets ( < 1.7 ~ { } R _ { \oplus } ) , where the metallicity difference is [ Fe/H ] \simeq 0.25 \pm 0.07 dex .
The excess of hot rocky planets around metal-rich stars implies they either share a formation mechanism with hot Jupiters , or trace a planet trap at the protoplanetary disk inner edge which is metallicity-dependent .
We do not find statistically significant evidence for a previously identified trend that small planets toward the habitable zone are preferentially found around low-metallicity stars .
Refuting or confirming this trend requires a larger sample of spectroscopic metallicities .