  There are several FeSe based superconductors, including the bulk FeSe,
monolayer FeSe thin film, intercalated KxFe2-ySe2 and Li1-xFexOHFeSe, etc.
Their normal states all show metallic behavior. The key player here is the FeSe
layer which exhibits the highest superconducting transition temperature in the
form of monolayer thin film. Recently a new FeSe based compound, CsFe4-xSe4
with the space group of Bmmm was found. Interestingly the system shows a strong
insulator-like behavior although it shares the same FeSe planes as other
relatives. Density functional theory calculations indicate that it should be a
metal, in sharp contrast with the experimental observations. Here we report the
emergence of unconventional superconductivity by applying pressure to suppress
this insulator-like behavior. At ambient pressure, the insulator-like behavior
cannot be modeled as a band insulator, but can be described by the
variable-range-hopping model for correlated systems. Furthermore, the specific
heat down to 400 mK has been measured and a significant residual coefficient
gamma_0=C/T|T->0 is observed, which contrasts the insulator-like state and
suggests some quantum freedom of spin dynamics. By applying pressure the
insulator-like behavior is gradually suppressed and the system becomes a metal,
finally superconductivity is achieved at about 5.1 K. The superconducting
transition strongly depends on magnetic field and applied current, indicating a
fragile superfluid density. Our results suggest that the superconductivity is
established by diluted Cooper pairs on top of a strong correlation background
in CsFe4-xSe4.
