Unraveling the Robust Superconductivity Phenomenon of High-Entropy Alloy

Recent experiments demonstrate a "robust superconductivity phenomenon" in niobium-based alloys, where the superconducting state remains intact and the critical temperature ($T_c$) is largely unaffected by external pressure well above tens of gigapascal (GPa) into the megabar regime ($\ge 100 GPa$). Motivated by these observations, we perform first-principles electron-phonon calculations for body-centered cubic Nb and NbTi crystals, as well as for special quasi-random structures of Nb$_{0.5}$Ti$_{0.5}$ and (NbTa)$_{0.7}$(HfZrTi)$_{0.3}$ high-entropy alloy (HEA). The calculations unravel the underlying mechanism of robust superconductivity, stemming from a compensation effect between varying electronic and phonon properties under pressure. The results also reveal how structural and chemical disorders modify the superconducting state. The first-principles $T_c$ values agree quantitatively with the experiments throughout the entire pressure range under study. Our work thereby paves the way for exploring superconducting HEAs under pressure via advanced first-principles simulations.