Electron-phonon superconductivity in the ternary phosphidesBaM2P2(M=Ni,Rh,and Ir)

Abstract

Ab initio plane-wave pseudopotential calculations of electronic and vibrational properties have been carried out for the ternary phosphides $\mathrm{Ba}{M}_{2}{\mathrm{P}}_{2}$ $(M=\text{Ni},\text{Rh}\text{ and Ir})$ with a ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure. The calculated electronic results show the metallic character of $\mathrm{Ba}{M}_{2}{\mathrm{P}}_{2}$, and the plots of total and partial density of states of $\mathrm{Ba}{M}_{2}{\mathrm{P}}_{2}$ exhibit strong hybridization between the $d$ states of the $M$ atom and the $p$ states of the P atom below the Fermi energy. Differences in the phonon spectrum and density of states both in the acoustical and optical ranges for these compounds are presented and discussed. The Eliashberg spectral function for these compounds has been calculated by using a linear response approach based on the density functional theory. By integrating the Eliashberg spectral function, the average electron-phonon coupling parameter $(\ensuremath{\lambda})$ is determined to be 0.61 for ${\mathrm{BaNi}}_{2}{\mathrm{P}}_{2}$, 0.55 for ${\mathrm{BaIr}}_{2}{\mathrm{P}}_{2}$, and 0.43 for ${\mathrm{BaRh}}_{2}{\mathrm{P}}_{2}$. Using the calculated values of $\ensuremath{\lambda}$ and the logarithmically averaged phonon frequency ${\ensuremath{\omega}}_{ln}$ the superconducting critical temperature $({T}_{c})$ values for ${\mathrm{BaNi}}_{2}{\mathrm{P}}_{2},{\mathrm{BaIr}}_{2}{\mathrm{P}}_{2}$, and ${\mathrm{BaRh}}_{2}{\mathrm{P}}_{2}$ are obtained to be 2.80, 1.97, and 0.70 K, respectively, which compare very well with their experimental values of 3.0, 2.1, and 1.0 K.