Transition metal nitrides (TMNs) have garnered significant attention for their outstanding mechanical properties and potential for superconductivity, particularly in zirconium nitride materials. This study investigates the impact of structural variations on the electronic and superconducting behavior of the Zr-N system using state-of-the-art density functional theory calculations. We analyze three thermodynamically stable phases: rock salt (Fm \(\overline{3 }\) m), tetragonal (P42/mnm), and orthorhombic (Pnma), as well as metastable trigonal ( \(R\overline{3 }c\) ), cubic (Fd \(\overline{3 }\) m), and hexagonal (P63/mmc) configurations. Electronic band structure calculations indicate conductivity in all phases except the cubic and orthorhombic Zr3N4 structures, which display insulating properties. Importantly, all metallic Zr-N crystalline phases exhibit both mechanical stability (validated by Born-Huang criteria) and dynamical stability (confirmed by phonon dispersion analysis). Kohn anomalies identified in the Fermi surface topology of Zr-N phases arise from Fermi surface nesting across distinct structural configurations. The rock salt and the hexagonal phases exhibit pronounced nesting vectors, which enhance electron–phonon coupling. This interaction is further evidenced by significant mode softening along high-symmetry directions in their dispersion spectra, a hallmark of strong electron–phonon interactions. We found that superconducting transition temperature Tc varies markedly with crystal symmetry. Our findings demonstrate a Tc of 11.7 K for the rock salt phase, 29.8 K for the hexagonal phase, 11.3 K for the tetragonal phase, and 8.1 K for the trigonal phase. The hexagonal phase’s elevated Tc underscores the critical role of lattice geometry in modulating superconductivity performance. Microscopically, superconductivity in Zr-N system stems from synergistic coupling between Zr d-electron states near the Fermi level and lattice vibrations, specifically, Zr acoustic and N optical phonons.
