Cocktail effect on superconductivity in hexagonal high-entropy alloys

We report the study of the cocktail effect on superconductivity in high-entropy alloys (HEAs), using hexagonal close-packed HEAs as a prototype system. Compared with the compositional averages of the constituent elements, the superconducting transition temperature ${T}_{\mathrm{c}}$ is enhanced by from a factor of about $2$ to over one order of magnitude. This ${T}_{\mathrm{c}}$ enhancement correlates with the reduction in the Debye temperature, underlining the importance of phonon softening in triggering the cocktail effect. Furthermore, we show that the ${T}_{\mathrm{c}}$ in these HEAs is governed by the average phonon frequency and electron-phonon coupling strength, the latter of which scales linearly with the inverse HEA molecular weight and is progressively weakened with increasing mixing entropy. Our study paves the way toward quantitative understanding of the superconductivity in HEAs.