title: Discovery of a superconducting high-entropy alloy.
abstract: High-entropy alloys (HEAs) are multicomponent mixtures of elements in similar concentrations, where the high entropy of mixing can stabilize disordered solid-solution phases with simple structures like a body-centered cubic or a face-centered cubic, in competition with ordered crystalline intermetallic phases. We have synthesized an HEA with the composition Ta34Nb33Hf8Zr14Ti11 (in at. %), which possesses an average body-centered cubic structure of lattice parameter a=3.36  Å. The measurements of the electrical resistivity, the magnetization and magnetic susceptibility, and the specific heat revealed that the Ta34Nb33Hf8Zr14Ti11 HEA is a type II superconductor with a transition temperature Tc≈7.3  K, an upper critical field μ0H_c2≈8.2  T, a lower critical field μ0Hc1≈32  mT, and an energy gap in the electronic density of states (DOS) at the Fermi level of 2Δ≈2.2  meV. The investigated HEA is close to a BCS-type phonon-mediated superconductor in the weak electron-phonon coupling limit, classifying it as a "dirty" superconductor. We show that the lattice degrees of freedom obey Vegard's rule of mixtures, indicating completely random mixing of the elements on the HEA lattice, whereas the electronic degrees of freedom do not obey this rule even approximately so that the electronic properties of a HEA are not a "cocktail" of properties of the constituent elements. The formation of a superconducting gap contributes to the electronic stabilization of the HEA state at low temperatures, where the entropic stabilization is ineffective, but the electronic energy gain due to the superconducting transition is too small for the global stabilization of the disordered state, which remains metastable.
authors.affiliation: Faculty of Mathematics and Physics, J. Stefan Institute and University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia.
authors.forename: P
authors.initials: P
authors.lastname: Koželj
authors.affiliation: Faculty of Mathematics and Physics, J. Stefan Institute and University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia.
authors.forename: S
authors.initials: S
authors.lastname: Vrtnik
authors.affiliation: Faculty of Mathematics and Physics, J. Stefan Institute and University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia.
authors.forename: A
authors.initials: A
authors.lastname: Jelen
authors.affiliation: Faculty of Mathematics and Physics, J. Stefan Institute and University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia.
authors.forename: S
authors.initials: S
authors.lastname: Jazbec
authors.affiliation: Faculty of Civil and Geodetic Engineering, Institute of Mathematics, Physics and Mechanics and University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.
authors.forename: Z
authors.initials: Z
authors.lastname: Jagličić
authors.affiliation: Department of Materials, Laboratory of Crystallography, ETH Zürich, Vladimir-Prelog-Weg 5, CH-8093 Zürich, Switzerland.
authors.forename: S
authors.initials: S
authors.lastname: Maiti
authors.affiliation: Institut für Mikrostrukturforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Feuerbacher
authors.affiliation: Department of Materials, Laboratory of Crystallography, ETH Zürich, Vladimir-Prelog-Weg 5, CH-8093 Zürich, Switzerland.
authors.forename: W
authors.initials: W
authors.lastname: Steurer
authors.affiliation: Faculty of Mathematics and Physics, J. Stefan Institute and University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia.
authors.forename: J
authors.initials: J
authors.lastname: Dolinšek