Cr _2 AlN and the search for the highest temperature superconductor in the M _2 AX family

We have developed a high-throughput computational method to predict the superconducting transition temperature in stable hexagonal M _2 AX phases, and applied it to all the known possible choices for M (M: Sc, Ti, V, Cr, Mn, Fe, Y, Zr, Nb, Mo, Lu, Hf and Ta). We combine this with the best candidates for A (A: Al, Cu, Ge and Sn ) and X (X: C and N) from our previous work, and predict T _c for 60 M _2 AX-phase materials, 53 of which have never been studied before. From all of these, we identify Cr _2 AlN as the best candidate for the highest T _c , and confirm its high T _c with more detailed density functional theory electron-phonon coupling calculations. Our detailed calculations predict T_c = 14.8 K for Cr _2 AlN, which is significantly higher than any T_c value known or predicted for any material in the M _2 AX family to date.