  Pressure plays an essential role in the induction1 and control2,3 of
superconductivity in iron-based superconductors. Substitution of a smaller
rare-earth ion for the bigger one to simulate the pressure effects has
surprisingly raised the superconducting transition temperature Tc to the record
high 55 K in these materials4,5. However, Tc always goes down after passing
through a maximum at some pressure and the superconductivity eventually tends
to disappear at sufficiently high pressures1-3. Here we show that the
superconductivity can reemerge with a much higher Tc after its destruction upon
compression from the ambient-condition value of around 31 K in newly discovered
iron chalcogenide superconductors. We find that in the second superconducting
phase the maximum Tc is as high as 48.7 K for K0.8Fe1.70Se2 and 48 K for
(Tl0.6Rb0.4)Fe1.67Se2, setting the new Tc record in chalcogenide
superconductors. The presence of the second superconducting phase is proposed
to be related to pressure-induced quantum criticality. Our findings point to
the potential route to the further achievement of high-Tc superconductivity in
iron-based and other superconductors.
