Characterisation of spin-orbit effects in superconductors In5Bi3 and In5Sb3

We report a first principles computational analysis of two phonon-mediated superconductors, In5Bi3 and In5Sb3. 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 In5Bi3, 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 In5Sb3, 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.