Superconductivity by doping in alkali-metal hydrides without applied pressure: An ab initio study

The electronic, lattice dynamical, electron-phonon coupling, and superconducting properties of alkali-metal hydrides LiH, NaH, and KH, metalized through doping with alkaline-earth metals Be, Mg, and Ca, respectively, are investigated within the framework of density functional perturbation theory. The alloys were modeled by the self-consistent virtual crystal approximation, and the effect of zero-point energy contribution is consistently taken into account. For all three alloys, a steady increase of the electron-phonon coupling constant $\ensuremath{\lambda}$ is found with progressive alkaline-earth metal doping, reaching values as high as 0.47 for (Li/Be)H, 1.26 for (Na/Mg)H, and 1.69 for (K/Ca)H. The growth of $\ensuremath{\lambda}$ with doping is the result of two effects: the softening of the phonon spectrum, mainly of the H-optical modes, and the increase of the density of states at the Fermi level. Estimates of the superconducting critical temperature reach values of 2.1 K for ${\mathrm{Li}}_{0.95}{\mathrm{Be}}_{0.05}\mathrm{H}$, 28 K for ${\mathrm{Na}}_{0.8}{\mathrm{Mg}}_{0.2}\mathrm{H}$, and even 49 K for ${\mathrm{K}}_{0.55}{\mathrm{Ca}}_{0.45}\mathrm{H}$, demonstrating that doping is an alternative route to high transition temperatures in this material class without the need to apply high external pressure.