  We discover a population of short-period, Neptune-size planets sharing key
similarities with hot Jupiters: both populations are preferentially hosted by
metal-rich stars, and both are preferentially found in Kepler systems with
single transiting planets. We use accurate LAMOST DR4 stellar parameters for
main-sequence stars to study the distributions of short-period 1d < P < 10d
Kepler planets as a function of host star metallicity. The radius distribution
of planets around metal-rich stars is more "puffed up" as compared to that
around metal-poor hosts. In two period-radius regimes, planets preferentially
reside around metal-rich stars, while there are hardly any planets around
metal-poor stars. One is the well-known hot Jupiters, and the other is a
population of Neptune-size planets (2 R_Earth <~ R_p <~ 6 R_Earth), dubbed as
"Hoptunes". Also like hot Jupiters, Hoptunes occur more frequently in systems
with single transiting planets though the fraction of Hoptunes occurring in
multiples is larger than that of hot Jupiters. About 1% of solar-type stars
host "Hoptunes", and the frequencies of Hoptunes and hot Jupiters increase with
consistent trends as a function of [Fe/H]. In the planet radius distribution,
hot Jupiters and Hoptunes are separated by a "valley" at approximately Saturn
size (in the range of 6 R_Earth <~ R_p <~ 10 R_Earth), and this "hot-Saturn
valley" represents approximately an order-of-magnitude decrease in planet
frequency compared to hot Jupiters and Hoptunes. The empirical "kinship"
between Hoptunes and hot Jupiters suggests likely common processes (migration
and/or formation) responsible for their existence.
