The compliance of the molecular hydride superconductor $BiH_4$ with the Migdal's theorem

The discovery of near-room-temperature superconductivity in H3S sparked experimental and theoretical studies of highly compressed hydrides with the aim of obtaining room-temperature superconductivity. There are two dominant hydride classes where the search is ongoing: the first class is the covalently bonded hydrides (which is represented by H3S), and the second class is the clathrate-type hydrides (which is represented by LaH10, YH6, CaH6). Recently, the third class of superconducting hydrides, where the hydrogen remains its molecular form, has been discovered. This class is represented by BaH12 and BiH4. Here, we analyzed experimental data for the BaH12 and BiH4. We found that the BaH12 exhibits grains of an average size of 26 nm and a low level of microstrain 0.1%, in the range of 126 GPa < P < 160 GPa. We also derived the Debye $Θ_D$ and Einstein $Θ_E$ temperatures, and the electron-phonon coupling constant $Λ_{e-ph} $ in BaH12 and BiH4. The $Λ_{e-ph} $ in BiH4 significantly differs from the values obtained by first-principles calculations. The derived Fermi temperature $T_F = 20,000 K$ for BiH4 positions this molecular hydride between the unconventional and conventional superconductors bands in the Uemura plot. This position is outside of the band where covalently bonded and clathrate hydrides are located. The ratio $Θ_D / T_F = 0.026 $ of BiH4 is typical for pure metals and A-15 alloys. This implies that the BiH4, is the first hydride superconductor which complains with the Migdal's theorem.