Significance: High-entropy alloys are a new class of materials that consist of several principal elements arranged on simple lattices. These structures are stabilized by the high configurational entropy of the random mixing of the elements. Here, we show that the properties of a superconducting high-entropy alloy are strongly related to the electron count and that the superconducting transition temperatures of these alloys fall between those of analogous crystalline and amorphous materials. We find that despite the large degree of randomness and disorder in these alloys, the superconducting properties are nevertheless strongly dependent on the chemical composition and complexity. We argue that high-entropy alloys are excellent model systems for understanding how superconductivity and other collective quantum states evolve from crystals to amorphous solids.

Polycrystalline samples of four intermetallic compounds: $M{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$ ($M=\mathrm{Sc}$, Y, La, and Lu) were synthesized using an arc-melting technique. The crystal structures were analyzed by means of powder x-ray diffraction and Rietveld analysis, and the physical properties were studied by means of heat capacity, electrical resistivity, and magnetic susceptibility measurements down to 0.4 K. For $\mathrm{Sc}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}, \mathrm{Lu}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$, and $\mathrm{Y}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$, superconductivity was observed with critical temperatures $T_{\mathrm{c}}=1.00$, 0.57, and 0.60 K, respectively. Superconductivity for the Lu compound is reported. Theoretical calculations of the electronic and phonon structures were conducted in order to analyze the superconductivity and dynamics in $\mathrm{Sc}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}, \mathrm{Y}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$, and $\mathrm{Lu}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$ and to explain the lack of a superconducting transition in $\mathrm{La}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$ down to 0.4 K. The results of the experimental and theoretical studies show that all the compounds are weakly coupled type-II BCS superconductors, and reveal the importance of the $M$-atom anharmonic “rattling” modes for the superconductivity in these materials, which seem to enhance $T_{\mathrm{c}}$, especially for $\mathrm{Sc}{\mathrm{V}}_2\mathrm{A}{\mathrm{l}}_{20}$.