Doping effects on the stability and superconductivity of penta-graphene-like ZrH10 and HfH10 under pressure

The discovery of room-temperature superconductors has aroused great attention in pressure-induced superhydrides. Herein we explore the doping effects on the newly proposed penta-graphene-like hydrides ${\mathrm{ZrH}}_{10}$ and ${\mathrm{HfH}}_{10}$ from first-principles calculations. Imaginary phonon frequencies of $P{6}_{3}/mmc\phantom{\rule{4pt}{0ex}}{\mathrm{ZrH}}_{10}$ and ${\mathrm{HfH}}_{10}$ at lower pressures are found to be eliminated by hole doping, leading to more accessible superconductivity. At high pressures, phonons are prone to be softened by electron doping, which increases the electron-phonon coupling and the superconducting critical temperature (${T}_{c}$). Doping is found to be an effective way to lower the stabilization pressure and increase the ${T}_{c}$ of $P{6}_{3}/mmc\phantom{\rule{4pt}{0ex}}{\mathrm{ZrH}}_{10}$ and ${\mathrm{HfH}}_{10}$. This work paves an avenue for realizing low-pressure high-${T}_{c}$ superconducting hydrides.