Pressure-induced multiple phase transformations of the BaBi$_3$ superconductor

Measurements of temperature-dependent resistance and magnetization under hydrostatic pressures up to 2.13 GPa are reported for single-crystalline, superconducting BaBi$_3$. A temperature - pressure phase diagram is determined and the results suggest three different superconducting phases $α$, $β$, and $γ$ in the studied pressure range. We further show that occurrence of the three superconducting phases is intuitively linked to phase transitions at higher temperature which are likely first order in nature. $T_p$, which separates phase $α$ from $β$ and $γ$, is associated with an abrupt resistance change as pressure is increased from 0.27 GPa to 0.33 GPa. Above 0.33 GPa, an "S-shape" anomaly in the temperature-dependent resistance curve, $T_\text S$, is observed and associated with the transition between the $β$ and $γ$ phases. Further increasing of pressure above 1.05 GPa suppresses this transition and BaBi$_3$ stays in $γ$ phase over the whole investigated temperature range. These high-temperature anomalies are likely related to structural degrees of freedom. With the $α$ phase being the ambient-pressure tetragonal structure ($P4/mmm$), our first-principle calculations suggest the $β$ phase to be cubic structure ($Pm-3m$) and the $γ$ phase to be a distorted tetragonal structure where the Bi atoms are moved out of the face-centered position. Finally, an analysis of the evolution of the superconducting upper critical field with pressure further confirms these transitions in the superconducting state and suggests a possible change of band structure or a Lifshitz transition near 1.54 GPa in $γ$ phase. Given the large atomic numbers of both Ba and Bi, our results establish BaBi$_3$ as a good candidate for the study of the interplay of structure with superconductivity in the presence of strong spin-orbit coupling.