Topological states in A15 superconductors

Superconductors with the A15 structure are prototypical type-II $s$-wave superconductors which have generated considerable interest in early superconducting material history. However, the topological nature of the electronic structure remains unnoticed so far. Here, using first-principles band structure calculations based on density-functional theory, we show that the A15 superconductors (${\mathrm{Ta}}_{3}\mathrm{Sb}$, ${\mathrm{Ta}}_{3}\mathrm{Sn}$, and ${\mathrm{Ta}}_{3}\mathrm{Pb}$) have nontrivial band topology in the bulk electronic band structures, leading to the formation of topological surface states near the Fermi energy. Due to the bulk superconductivity, the proximity effect in the topological surface states would induce topological superconductivity even without heterostructure of a topological insulator and an $s$-wave superconductor. Our results indicate that the A15 superconductors are promising candidates for the realization of the topological superconductivity and the Majorana fermion.