Theoretical analysis of spin–orbit coupling-weakened superconductivity in Bi-rich Ba2Bi3 compounds

Abstract

We present a comprehensive first-principles investigation of the structural, electronic, elastic, lattice-dynamical, and electron–phonon interaction properties of the Bi-rich superconductor Ba₂Bi₃, with particular emphasis on the role of spin–orbit coupling (SOC). Calculations are performed within density-functional theory and density-functional perturbation theory using the generalized gradient approximation, considering both scalar-relativistic (non-SOC) and fully relativistic (SOC-included) frameworks. While SOC induces only moderate modifications in the electronic band structure, phonon dispersions, and elastic properties, it has a pronounced impact on the electron–phonon interaction. Specifically, the electron–phonon coupling constant λ is found to decrease significantly from 1.32 to 0.88 (∼33%) upon inclusion of SOC. As a consequence, the superconducting transition temperature T_c is suppressed from 6.7 K to 4.1 K, bringing the theoretical prediction into close agreement with the experimental value of 4.4 K. A detailed analysis reveals that this SOC-induced weakening of superconductivity originates predominantly from a reduction in the electron–phonon coupling matrix elements, rather than from changes in the electronic density of states at the Fermi level or phonon frequencies. Our results demonstrate that superconductivity in Ba₂Bi₃ is an intrinsic property of the Bi ribbon networks and highlight the essential role of relativistic effects in accurately describing electron–phonon-mediated superconductivity in Bi-based compounds containing heavy elements.