Spin-orbit coupling enhanced superconductivity in Bi-rich compounds ABi$_{3}$ (A=Sr and Ba)

Recently, Bi-based compounds have attracted attentions because of the strong spin-orbit coupling (SOC). In this work, we figured out the role of SOC in ABi$_{3}$ (A=Sr and Ba) by theoretical investigation of the band structures, phonon properties, and electron-phonon coupling. Without SOC, strong Fermi surface nesting leads to phonon instabilities in ABi$_{3}$. SOC suppresses the nesting and stabilizes the structure. Moreover, without SOC the calculation largely underestimates the superconducting transition temperatures ($T_{c}$), while with SOC the calculated $T_{c}$ are very close to those determined by measurements on single crystal samples. The SOC enhanced superconductivity in ABi$_{3}$ is due to not only the SOC induced phonon softening, but also the SOC related increase of electron-phonon coupling matrix elements. ABi$_{3}$ can be potential platforms to construct heterostructure of superconductor/topological insulator to realize topological superconductivity.