Superconductivity and unexpected chemistry of germanium hydrides under pressure

Following the idea that hydrogen-rich compounds might be high-T$_c$ superconductors at high pressures, and the very recent breakthrough in predicting and synthesizing hydrogen sulfide with record-high T$_c$ = 203 K, ab initio evolutionary algorithm for crystal structure prediction was employed to find stable germanium hydrides. In addition to the earlier structure of germane with space group Ama2, we propose a new C2/m structure, which is energetically more favorable at pressures above 278 GPa (with inclusion of zero point energy). Our calculations indicate metallicity of the new C2/m phase of germane with T$_c$ = 67 K at 280 GPa. Germane is found to exhibit thermodynamic instability to decomposition to hydrogen and the new compound Ge$_3$H$_{11}$ at pressures above 300 GPa. Ge$_3$H$_{11}$ with space group I$\bar{4}$m2 is found to become stable at above 285 GPa with T$_c$ = 43 K. We find that the pressure-induced phase stability of germanium hydrides is distinct from its analogous isoelectronic systems, e.g., Si-hydrides and Sn-hydrides. Superconductivity stems from large electron-phonon coupling associated with the wagging, bending and stretching intermediate-frequency modes derived mainly from hydrogen.