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

Superconductivity and unexpected chemistry of germanium hydrides under pressure