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.
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