Superconducting and Anisotropic Properties of Ti-Hf-Nb-Ta-Re High-Entropy Alloy Superconductors

The Ti-Hf-Nb-Ta-Re high-entropy alloy (HEA) superconductor exhibits remarkable superconducting properties with critical temperatures (T_c) ranging from 3.25 K to 4.38 K. This work presents a comprehensive analysis of its anisotropic energy density (E*), critical current density (J_c), and upper critical field (H_c2) through both empirical modeling and crystallographic approaches. We establish quantitative relationships between the magnetic anisotropy energy and measurable superconducting parameters, demonstrating that the weak anisotropy (E* ≈ -1.13) leads to near-isotropic behavior in H_c2 and J_c.