Rhenium-based superconductors have recently attracted significant interest due to their unconventional superconducting properties. In this work, we report the synthesis and properties of new superconducting ReX (X = Nb, Ta, Ti, Zr, Hf) binary alloys which maintain a fixed composition of rhenium while crystallizing in centrosymmetric to non-centrosymmetric crystal structures, depending on the elements of the X site. Comprehensive structural and superconducting properties were investigated using powder x-ray diffraction, AC transport, magnetization, and specific heat measurements, and on the basis of these measurements, the superconducting phase diagram was constructed. The results suggest a complex interplay of crystal structure and the Re/X ratio, which governs the strength of spin-orbital coupling and controls the unconventional superconducting behavior in Re-based superconductors.

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