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We have investigated the structural, electronic, mechanical, phononic, andsuperconducting properties of the Zr$_2$Ir compound with a body-centeredtetragonal crystal structure using first-principles calculations. Our analysisreveals that the Zr$_2$Ir compound shows mechanical and dynamically stable byusing with and without spin-orbit coupling (SOC) effect. After calculating someproperties such as elastic constants, Bulk modulus, Young's modulus, Poissonratio, Debye temperature, and sound velocity, we found that Zr$_2$Ir isductile. When the elastic constants $C_{11}$ and $C_{33}$ are compared, it isdetermined that the situation changes in the opposite direction under theeffect of SOC, that is, more compressibility along the x-axis turns into thez-axis. Here, the electronic band structure and intensity of the statescalculated for the compound show a metallic character. The superconductingcritical temperature ($T_c$) and electron-phonon coupling constant ($\lambda$)were found to be 7.50 K and 0.93 without SOC and 7.62 K and 0.96 with SOC,respectively. We determined that although the Zr$_2$Ir compound has a strongelectron-phonon coupling regime, the inclusion of SOC slightly reduces itscritical temperature and electron-phonon coupling constant.

Atomic, electronic, and superconducting properties of Zr$_2$Ir compound