Discovery of a Superconducting High-Entropy Alloy

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 ${\mathrm{Ta}}_{34}{\mathrm{Nb}}_{33}{\mathrm{Hf}}_8{\mathrm{Zr}}_{14}{\mathrm{Ti}}_{11}$ (in at. %), which possesses an average body-centered cubic structure of lattice parameter $a=3.36\AA$. The measurements of the electrical resistivity, the magnetization and magnetic susceptibility, and the specific heat revealed that the ${\mathrm{Ta}}_{34}{\mathrm{Nb}}_{33}{\mathrm{Hf}}_8{\mathrm{Zr}}_{14}{\mathrm{Ti}}_{11}$ HEA is a type II superconductor with a transition temperature $T_c\approx 7.3\mathrm{K}$, an upper critical field ${\mu }_0{H}_{c2}\approx 8.2\mathrm{T}$, a lower critical field ${\mu }_0{H}_{c1}\approx 32\mathrm{mT}$, and an energy gap in the electronic density of states (DOS) at the Fermi level of $2\mathrm{\Delta }\approx 2.2\mathrm{meV}$. 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.

Figure 1

X-ray diffraction pattern of the ${\mathrm{Ta}}_{34}{\mathrm{Nb}}_{33}{\mathrm{Hf}}_8{\mathrm{Zr}}_{14}{\mathrm{Ti}}_{11}$ HEA. The peaks are indexed to a bcc crystal lattice.

Figure 2

Electrical resistivity in zero magnetic field between 300 and 2 K. Magnetic-field dependence of the resistivity in the region of the SC transition for fields up to 9 T is shown in the inset.

Figure 3

The zfc magnetic susceptibility $\chi =M/H$ in a 5 mT field in the region of the SC transition. The inset shows isothermal magnetization $M(H)$ in the low-field range at temperatures between 2 and 8 K. The arrow denotes the lower critical field $H_{c1}$ at $T=2\mathrm{K}$.

Figure 4

(a) Low-temperature specific heat $C(T)$ for selected magnetic fields. The inset shows a semilog graph of $C_{es}/\gamma T_c$ against $T_c/T$ and solid line is the fit $C_{es}/\gamma T_c=7.9\exp (-1.54T/T_c)$. (b) Specific heat in zero field and 9 T in a $C/T$ versus $T^2$ plot. The inset shows the upper critical field ${\mu }_0{H}_{c2}(T)$.