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The implementation of electron- and hole-doping, in conjunction to appliedpressure, is analyzed as a mechanism to induce or enhance the superconductingstate on fcc YH$_3$ and ScH$_3$. In particular, the evolution of theirstructural, electronic, and lattice dynamical properties, as well as theelectron-phonon coupling and superconducting critical temperature ($T_c$) ispresented and discussed, as a function of the electron- and hole-doping contentas well as applied pressure. The study was performed within the densityfunctional perturbation theory, taking into account the effects of zero-pointenergy through the quasi-harmonic approximation, while the doping wasimplemented by means of the construction of the Sc$_{1-x}$M$_{x}$H$_{3}$(M=Ca,Ti) and Y$_{1-x}$M$_{x}$H$_{3}$ (M=Sr,Zr) solid solutions modeled withthe virtual crystal approximation (VCA). We found that the ScH$_3$ and YH$_3$hydrides shown a significant improvement of their electron-phonon couplingproperties under hole-doping (M=Ca,Sr) and at pressure values close todynamical instabilities. Instead, by electron-doping (M=Ti,Zr), the systems donot improve such properties, whatever value of applied pressure is considered.Then, as a result, $T_c$ rapidly increases as a function of $x$ on thehole-doping region, reaching its maximum value of $92.7(67.9)$~K and$84.5(60.2)$~K at $x=0.3$ for Sc$_{1-x}$Ca$_{x}$H$_{3}$ at $10.8$~GPa andY$_{1-x}$Sr$_{x}$H$_{3}$ at $5.8$~GPa respectively, with $\mu^{*}=0(0.15)$,while for both, electron- and hole-doping, $T_c$ decreases as a function of theapplied pressure, mainly due to phonon hardening. By the thorough analysis ofthe electron-phonon properties as a function of doping and pressure, we canconclude that the tuning of the lattice dynamics is a promising path forimproving the superconductivity on both systems.

chinese journal of physics

Superconductivity on ScH$_{3}$ and YH$_{3}$ hydrides: Effects of applied  pressure in combination with electron- and hole-doping on the electron-phonon  coupling properties