Fermi surface topology and anisotropic superconducting gap in electron-doped hydride compounds at high pressure

Abstract

The recent theoretical discovery of the predicted high-temperature superconductivity (superconducting transition temperature ${T}_{\mathrm{c}}\ensuremath{\sim}351\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ at 300 GPa) in clathrate ${\mathrm{Li}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ is an important advance toward room-temperature superconductors. Here we use first-principle approaches to identify a new ternary hydride of clathrate structure of $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ by Rb-doped $\mathrm{Mg}{\mathrm{H}}_{16}$ at 300 GPa. We first verified the thermal and dynamic stability for the $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ through the formation enthalpy and phonon calculations, respectively. Next, we showcased that $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ has two Fermi surface (FS) sheets, which are both dominated by the H2 $s$ orbital. Using the Eliashberg formalism, the ${T}_{\mathrm{c}}$ of $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ was calculated to be 130 K at 300 GPa. Furthermore, the calculations of the electronic, phonon, and superconducting properties reveal that $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ has four FS sheets with mixed H1 $s$ and H2 $s$ orbital character and reaches the ${T}_{\mathrm{c}}$ of 352 K at 300 GPa. Compared with $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$, $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ produces high-frequency phonon softening, leading to the enhancement of ${T}_{\mathrm{c}}$. Moreover, it is demonstrated that Rb substitution for Li produces the reduction of contribution of H orbitals to the FS sheets and the decrease in FS sheets in number, which tend to decrease the electron-phonon coupling strength and ${T}_{\mathrm{c}}$. Our observed FS sheets and their associated superconducting gap will provide key insights into the understanding of the superconductivity mechanism in these and related systems.