First-principles evidence for conventional superconductivity in a quasicrystal approximant

Quasicrystals (QCs) host long-range order without translational symmetry, a regime in which the very foundations of BCS theory are not straightforwardly applicable, yet experiments on QCs and their approximant crystals (ACs) point to conventional, s -wave, electron–phonon-coupled superconductivity. Here, we test the predictive power of the electron–phonon framework in a representative decagonal AC from first principles. Using state-of-the-art methods, we compute the superconducting properties of the recently discovered AC Al 13 Os 4 and quantitatively reproduce its bulk T c . This provides an determination of T c for an AC and establishes that the electron–phonon framework is predictive in these systems. Using the generalized quasichemical approximation for alloy modeling in the decagonal Al–Os family, we predict tunable superconductivity in Al 13 Os 4 − x Re x and Al 13 Os 4 − x Ir x ; in particular, Al 13 Re 4 is dynamically stable and estimated to have a T c about 30% above that of Al 13 Os 4 . Finally, we discuss the role of ACs as high-fidelity proxies for their parent QCs. Although long-range quasiperiodicity may introduce subtle electronic features, our findings indicate that the key ingredients for superconductivity are already encoded in the local structural motifs preserved by the AC. This places the Al–Os and Al–Re families among the most promising candidates for the highest- T c quasicrystalline superconductivity.