Superconductivity with large upper critical field in noncentrosymmetric Cr-bearing high-entropy alloys

A series of new Cr${}_{5+x}$Mo${}_{35-x}$W${}_{12}$Re${}_{35}$Ru${}_{13}$C${}_{20}$ high-entropy alloys (HEAs) have been synthesized and characterized by x-ray diffraction, scanning electron microscopy, electrical resistivity, magnetic susceptibility and specific heat measurements. It is found that the HEAs adopt a noncentrosymmetric cubic $\beta$-Mn type structure and exhibit bulk superconductivity for 0 $\le$ $x$ $\le$ 9. With increasing $x$, the cubic lattice parameter decreases from 6.7940(3) Å to 6.7516(3) Å. Meanwhile, the superconducting transition temperature $T_{\mathrm{c}}$ is suppressed from 5.49 K to 3.35 K due to the magnetic pair breaking caused by Cr moments. For all these noncentrosymmetric HEAs, the zero-temperature upper critical field $B_{\mathrm{c}2}$(0) is comparable to Pauli paramagnetic limit $B_{\mathrm{P}}$(0) = 1.86$T_{\mathrm{c}}$. In particular, the $B_{\mathrm{c}2}$(0)/$B_{\mathrm{P}}$(0) ratio reaches a maximum of $\sim$1.03 at $x$ = 6, which is among the highest for $\beta$-Mn type superconductors.