Electron- and hole-doping on ScH$_{2}$ and YH$_{2}$: Effects on superconductivity without applied pressure

We present the evolution of the structural, electronic, and lattice dynamical properties, as well as the electron-phonon coupling and superconducting critical temperature ($T_c$) of ScH$_2$ and YH$_2$ metal hydrides solid solutions, as a function of the electron- and hole-doping content. The study was performed within the density functional perturbation theory, taking into account the effect of zero-point energy through the quasi-harmonic approximation, and the solid solutions Sc$_{1-x}M_{x}$H$_{2}$ ($M$=Ca,Ti) and Y$_{1-x}M_{x}$H$_{2}$ ($M$=Sr,Zr) were modeled by the virtual crystal approximation. We have found that, under hole-doping ($M$=Ca,Sr), the ScH$_2$ and YH$_2$ hydrides do not improve their electron-phonon coupling properties, sensed by $\lambda(x)$. Instead, by electron-doping ($M$=Ti,Zr), the systems reach a critical content $x \approx 0.5$ where the latent coupling is triggered, increasing $\lambda$ as high as $70\%$, in comparison with its $\lambda(x=0)$ value. Our results show that $T_c$ quickly decreases as a function of $x$ on the hole-doping region, from $x=0.2$ to $x=0.9$, collapsing at the end. Alternatively, for electron-doping, $T_c$ first decreases steadily until $x=0.5$, reaching its minimum, but for $x > 0.5$ it increases rapidly, reaching its maximum value of the entire range at the Sc$_{0.05}$Ti$_{0.95}$H$_2$ and Y$_{0.2}$Zr$_{0.8}$H$_2$ solid solutions, demonstrating that electron-doping can improve the superconducting properties of pristine metal hydrides, in the absence of applied pressure.