On Distribution of Superconductivity in Metal Hydrides

Using the data on the superconducting critical temperature ($T_C$) for a number of metal hydrides, we found a rule that makes it possible to predict the maximum $T_C$ based only on the information about the electronic structure of metal atoms. Using this guiding principle, we explored the hydride systems for which no reliable information existed, predicted new higher hydrides in the K-H, Zr-H, Hf-H, Ti-H, Mg-H, Sr-H, Ba-H, Cs-H, and Rb-H systems at high pressures, and calculated their $T_C$. Results of the study of actinides and lanthanides show that they form highly symmetric superhydrides $XH_7-9$. However, actinide hydrides do not exhibit high-temperature superconductivity (except Th-H system) and might not be considered as promising materials for experimental studies, as well as all $d^m$-elements with m > 4, including metal hydrides of the noble elements. Designed neural network allowing the prediction of $T_C$ of various hydrides shows good accuracy and was used to estimate upper limit for $T_C$ of the materials with absence of the data. The developed rule, based on regular behavior of the maximum achievable critical temperature as a function of number of $d+f$ electrons, enables targeted predictions about the existence of new high-$T_C$ superconductors.