Tuning Superconductivity and Topological Bands in Ta–Nb–Hf–Zr–C Medium-Entropy Carbides by Valence Electron Concentration

Abstract The search for unconventional superconductors is a hot topic in materials science and condensed matter physics, yet remains challenging. Here we report a series of medium-entropy carbides (MECs) within the Ta–Nb–Hf–Zr–C system with finely tuned valence electron concentration (VEC). Through VEC engineering, the type-II Dirac points are deliberately shifted from approximately 0.19 eV below the Fermi level in the base composition Ta0.25Nb0.25Hf0.25Zr0.25C to within 6.7–59.1 meV of the Fermi level in the optimal composition Ta0.1875Nb0.1875Hf0.3125Zr0.3125C. All five compositions form single-phase rock-salt structures and exhibit type-II bulk superconductivity with TcMid ranging from 2.2 to 4.9 K. Among these, the equimolar Ta0.25Nb0.25Hf0.25Zr0.25C composition exhibits the highest Tc of 4.9 K, with μ0Hc2GL = 1.16 T, μ0Hc1(0) = 65.9 Oe, and ΔC/γTc = 1.16, alongside excellent stability in acidic/alkaline environments and under pressures up to 52 GPa. Our findings establish VEC engineering as a potentially transferable strategy for bridging topological band physics with superconductivity in medium/high-entropy ceramics, positioning this MEC family as a candidate platform for investigating topological superconductivity in disordered systems.