Mechanism of charge transport in lithium thiophosphate

Lithium ortho-thiophosphate (Li$_3$PS$_4$) has emerged as a promisingcandidate for solid-state-electrolyte batteries, thanks to its highlyconductive phases, cheap components, and large electrochemical stability range.Nonetheless, the microscopic mechanisms of Li-ion transport in Li$_3$PS$_4$ arefar to be fully understood, the role of PS$_4$ dynamics in charge transportstill being controversial. In this work, we build machine learning potentialstargeting state-of-the-art DFT references (PBEsol, r$^2$SCAN, and PBE0) totackle this problem in all known phases of Li$_3$PS$_4$ ($\alpha$, $\beta$ and$\gamma$), for large system sizes and timescales. We discuss the physicalorigin of the observed superionic behavior of Li$_3$PS$_4$: the activation ofPS$_4$ flipping drives a structural transition to a highly conductive phase,characterized by an increase of Li-site availability and by a drastic reductionin the activation energy of Li-ion diffusion. We also rule out any paddle-wheeleffects of PS$_4$ tetrahedra in the superionic phases -- previously claimed toenhance Li-ion diffusion -- due to the orders-of-magnitude difference betweenthe rate of PS$_4$ flips and Li-ion hops at all temperatures below melting. Wefinally elucidate the role of inter-ionic dynamical correlations in chargetransport, by highlighting the failure of the Nernst-Einstein approximation toestimate the electrical conductivity. Our results show a strong dependence onthe target DFT reference, with PBE0 yielding the best quantitative agreementwith experimental measurements not only for the electronic band-gap but alsofor the electrical conductivity of $\beta$- and $\alpha$-Li$_3$PS$_4$.