Structure- and composition-tunable superconductivity, band topology, and elastic response of hard binary niobium nitrides Nb2N, Nb4N3 and Nb4N5

We perform a systematic ab initio density functional study of the superconductivity, electronic and phononic band structures, electron-phonon coupling, and elastic constants of all four possible structures of niobium nitride fi-Nb2N as well as Nb-rich y-Nb4N3 and N-rich fi'-Nb4N5. First of all, we find that all four structures of fi-Nb2N are superconductors with superconducting transition temperatures (Tc) ranging from 0.6 to 6.1 K, depending on the structure. This explains why previous experiments reported contradicting Tc values for fi-Nb2N. Furthermore, both y-Nb4N3 and fi'-Nb4N5 are predicted to be superconductors with rather high Tc of 8.5 and 15.3 K, respectively. Second, the calculated elastic constants and phonon dispersion relations show that all the considered niobium nitride structures are mechanically and dynamically stable. Moreover, the calculated elastic moduli demonstrate that all the niobium nitrides are hard materials with bulk moduli and hardness being comparable to or larger than the well-known hard sapphire. Third, the calculated band structures reveal that the nitrides possess both type I and type II Dirac nodal points and are thus topological metals. Finally, the calculated electron-phonon coupling strength, superconductivity, and mechanical properties of the niobium nitrides are discussed in terms of their underlying electronic structures and also Debye temperatures. The present ab initio study thus indicates that fi-Nb2N, y-Nb4N3 and fi'-Nb4N5 are hard superconductors with nontrivial band topology and are promising materials for exploring exotic phenomena due to the interplay of hardness, superconductivity, and nontrivial band topology.