Enhanced $T_\mathrm{c}$ in eutectic high-entropy alloy superconductors Hf-Nb-Sc-Ti-Zr

The present investigation into the superconducting properties of eutectic high-entropy alloy (HEA) Hf-Nb-Sc-Ti-Zr systems reveals an enhanced superconducting critical temperature ($T_\mathrm{c}$) in body-centered cubic (bcc) phases compared to typical quinary bcc HEAs. In Hf$_{10}$Nb$_{25}$Sc$_{25}$Ti$_{20}$Zr$_{20}$, Hf$_{5}$Nb$_{45}$Sc$_{20}$Ti$_{15}$Zr$_{15}$, and Hf$_{5}$Nb$_{45}$Sc$_{10}$Ti$_{5}$Zr$_{35}$ systems, which span a broad range of valence electron concentration per atom, lattice strain and the presence of partial or absent eutectic phases are characteristic features at lower annealing temperatures. The eutectic regions expand rapidly following annealing at 600$^{\circ}$C in all systems. The $T_\mathrm{c}$ of each system increases markedly with rising annealing temperatures from 400$^{\circ}$C to 600$^{\circ}$C, reaching a maximum value of 9.93 K in the Hf$_{5}$Nb$_{45}$Sc$_{10}$Ti$_{5}$Zr$_{35}$ sample annealed at 800$^{\circ}$C. Nearly all samples can be classified as strong-coupling superconductors. The sample annealed at 500$^{\circ}$C in the Hf$_{5}$Nb$_{45}$Sc$_{10}$Ti$_{5}$Zr$_{35}$ system exhibits a critical current density ($J_\mathrm{c}$) exceeding the practical threshold of 10$^{5}$ A/cm$^{2}$ up to approximately 4 T at 4.2 K and 6 T at 2 K. The elevated $J_\mathrm{c}$ is attributed to significant lattice strain and phase instability. The underlying mechanism for the enhanced $T_\mathrm{c}$ in Hf-Nb-Sc-Ti-Zr systems is examined through specific heat data analysis, suggesting that the expansion of the eutectic regions induced by thermal annealing plays a pivotal role.