| Summary: | There are several FeSe based superconductors, including the bulk FeSe, monolayer FeSe thin film, intercalated K_{x}Fe_{2-y}Se_{2} and Li_{1-x}Fe_{x}OHFeSe, 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, CsFe_{4-x}Se_{4}, with the space group of Bmmm was found. Interestingly, the system shows a strong insulatorlike 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 insulatorlike behavior. At ambient pressure, the insulatorlike behavior cannot be modeled as a band insulator, but it 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 γ_{0}=C/T|_{T}_{→0} is observed, which contrasts the insulatorlike state and suggests some quantum freedom of spin dynamics. By applying pressure, the insulatorlike 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 CsFe_{4-x}Se_{4}.
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