Designing Quaternary Hydrides with Potential High T$_c$ Superconductivity

While hydrogen-rich materials have been demonstrated to exhibit high T$_c$ superconductivity at high pressures, there is an ongoing search for ternary and quaternary hydrides that achieve such high critical temperatures at much lower pressures. First-principles searches are impeded by the computational complexity of solving the Eliashberg equations for large, complex crystal structures. Here, we adopt a simplified approach using electronic indicators previously established to be correlated with superconductivity in hydrides. This is used to study complex hydride structures, which are predicted to exhibit promisingly high critical temperatures for superconductivity. In particular, we propose three classes of hydrides inspired by the FCC RH$_3$ structures that exhibit strong hydrogen network connectivity, as defined through the electron localization function. The first class [RH$_{11}$X$_3$Y] is based on a Pm$\overline{3}$m structure showing moderately high T$_c$, where the T$_c$ estimate from electronic properties is compared with direct Eliashberg calculations and found to be surprisingly accurate. The second class of structures [(RH$_{11}$)$_2$X$_6$YZ] improves on this with promisingly high density of states with dominant hydrogen character at the Fermi energy, typically enhancing T$_c$. The third class [(R$^1$H$_{11}$)(R$^2$H$_{11}$)X$_6$YZ] improves the strong hydrogen network connectivity by introducing anisotropy in the hydrogen network through a specific doping pattern. These model structures and the design principles provide the enough flexibility to optimize both T$_c$ and the structural stability of complex hydrides.