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Lacunar spinel GaTa$_4$Se$_8$ is a unique example of spin-orbit coupled Mottinsulator described by molecular $j_{\text{eff}}\!=\!3/2$ states. It becomessuperconducting at T$_c$=5.8K under pressure without doping. In this work, weshow, this pressure-induced superconductivity is a realization of a new typetopological phase characterized by spin-2 Cooper pairs. Starting fromfirst-principles density functional calculations and random phaseapproximation, we construct the microscopic model and perform the detailedanalysis. Applying pressure is found to trigger the virtual interband tunnelingprocesses assisted by strong Hund coupling, thereby stabilizing a particular$d$-wave quintet channel. Furthermore, we show that its Bogoliubovquasiparticles and their surface states exhibit novel topological nature. Toverify our theory, we propose unique experimental signatures that can bemeasured by Josephson junction transport and scanning tunneling microscope. Ourfindings open up new directions searching for exotic superconductivity inspin-orbit coupled materials.

Pressure Induced Topological Superconductivity in the Spin-Orbit Mott Insulator GaTa4Se8