Electron-phonon interaction and superconductivity in Tl-Pb-Bi alloys from first principles: Importance of spin-orbit coupling

The importance of spin-orbit coupling for lattice dynamics, electron-phonon coupling, and superconducting properties of face-centered cubic Tl-Pb-Bi alloys is investigated from first principles based on density-functional perturbation theory and a mixed-basis pseudopotential method. The alloys are modeled by the virtual crystal approximation. Electron-phonon coupling and superconducting properties are analyzed within the framework of the strong-coupling Eliashberg theory. A large increase of the coupling constant lambda for Bi doping can be traced back to a progressive softening of the phonon spectrum, signaling an incipient lattice instability. Performing calculations with and without spin-orbit interaction, we found a profound influence of this relativistic correction on the coupling strength, enhancing in most cases the coupling constant lambda by as much as 50%, but reducing it for Tl-rich alloys. For the whole alloy series, spin-orbit interaction impressively improves the agreement with both experimental phonon spectra as well as with superconducting quantities obtained from tunneling spectroscopy measurements, which at the same time demonstrates the applicability of the virtual crystal approximation.