Effects of spin-orbit coupling on the electron-phonon superconductivity in the cubic Laves-phase compounds CaIr2 and CaRh2

Abstract

We report our ab initio pseudopotential results for the structural, electronic, vibrational, and electron-phonon interaction properties of the cubic Laves-phase compounds CaIr2 and CaRh2. While the spin-orbit coupling (SOC) does not result in any appreciable changes in structural parameters, it lifts the degeneracies of some bands near the Fermi level, albeit with a much smaller amount for CaRh2. The effect of SOC on the vibrational properties of both materials is considerable. The SOC results in a slight decrease in the electronic density of states near the Fermi level N(EF) and makes low-frequency phonon branches harder, and the electron-phonon coupling parameter λ is lowered from 1.43 to 1.05 for CaIr2 and from 1.17 to 0.96 for CaRh2. On the other hand, the logarithmically averaged phonon frequency ωln is enhanced from 79.60 to 100.97 K for CaIr2 and from 120.20 to 140.80 K for CaRh2 with the inclusion of SOC. Using the calculated values of λ and ωln, the superconducting critical temperature is determined to be 5.94 K (7.34 K without SOC) for CaIr2 and 6.97 K (9.08 K without SOC) for CaRh2. The superconducting critical-temperature values with SOC compare very well with corresponding experimental values of 5.80 and 6.40 K, indicating the importance of SOC for the physical properties of both materials.