Cr[Formula: see text] AlN and the search for the highest temperature superconductor in the M[Formula: see text] AX family

We have developed a high-throughput computational method to predict the superconducting transition temperature in stable hexagonal M[Formula: see text] 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[Formula: see text] for 60 M[Formula: see text] AX-phase materials, 53 of which have never been studied before. From all of these, we identify Cr[Formula: see text] AlN as the best candidate for the highest T[Formula: see text] , and confirm its high T[Formula: see text] with more detailed density functional theory electron-phonon coupling calculations. Our detailed calculations predict [Formula: see text] = 14.8 K for Cr[Formula: see text] AlN, which is significantly higher than any [Formula: see text] value known or predicted for any material in the M[Formula: see text] AX family to date.