Emergence of Superconductivity at 20 K in Th$_3$P$_4$-type In$_{3-x}$S$_4$ Synthesized by Diamond Anvil Cell with Boron-doped Diamond Electrodes

The exploration of superconductors in metastable phases by manipulating crystal structures through high-pressure techniques has attracted significant interest in materials science to achieve a high critical temperature ($T_c$). In this study, we report an emergence of novel superconductivity in a metastable phase of Th$_3$P$_4$-type cubic In$_{3-x}$S$_4$ with remarkably high $T_c$ at 20 K under 45 GPa by using an originally designed diamond anvil cell equipped with boron-doped diamond electrodes, which can perform a high-pressure synthesis and an in-situ electrical transport measurement simultaneously. In-situ structural analysis indicates that the In$_{3-x}$S$_4$ appears partially above 40 GPa without heating. The high-pressure annealing treatment induces complete transformation to the Th$_3$P$_4$-type structure, and the defected concentration of x in In$_{3-x}$S$_4$ decreases with increasing annealing temperature. The $T_c$ in In$_{3-x}$S$_4$ is maximized at x = 0 and approaches 20 K. Electronic band calculations show that the high density of states composed of sulfur and indium bands are located at the conduction band bottom near Fermi energy. The record high $T_c$ in In$_{3-x}$S$_4$ among superconducting sulfides accelerates the further exploration of high $T_c$ materials within the Th$_3$P$_4$-type cubic family by using flexibility in crystal structure.