Collapse of metallicity and high-T_c superconductivity in the high-pressure phase of FeSe_0.89S_0.11

We investigate the high-pressure phase of the iron-based superconductor FeSe_0.89S_0.11 using transport and tunnel diode oscillator studies using diamond anvil cells. We construct detailed pressure-temperature phase diagrams that indicate that the superconducting critical temperature is strongly enhanced by more than a factor of four towards 40 K above 4 GPa. The resistivity data reveal signatures of a fan-like structure of non-Fermi liquid behaviour which could indicate the existence of a putative quantum critical point buried underneath the superconducting dome around 4.3 GPa. With further increasing the pressure, the zero-field electrical resistivity develops a non-metallic temperature dependence and the superconducting transition broadens significantly. Eventually, the system fails to reach a fully zero-resistance state, and the finite resistance at low temperatures becomes strongly current-dependent. Our results suggest that the high-pressure, high-T_c phase of iron chalcogenides is very fragile and sensitive to uniaxial effects of the pressure medium, cell design and sample thickness. This high-pressure region could be understood assuming a real-space phase separation caused by nearly concomitant electronic and structural instabilities.