Characterisation of spin–orbit effects in superconductors In₅Bi₃ and In₅Sb₃

Abstract We report a first principles computational analysis of two phonon-mediated superconductors, In 5 Bi 3 and In 5 Sb 3 . We show that spin–orbit coupling (SOC) leads to splitting of electron bands around the Fermi energy, resulting in a suppression of the electronic density of states in both compounds. In In 5 Bi 3 , the SOC is essential for the dynamical stability of the experimentally observed phase, and the calculated superconducting critical temperature is in close agreement with measurements. In In 5 Sb 3 , the SOC significantly reduces the calculated superconducting critical temperature compared to calculations neglecting relativistic effects. Our work emphasises the subtle interplay between spin–orbit interactions and phonon-mediated superconductivity.