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(E-F) and makes low-frequency phonon branches harder, and the electron-phonon coupling parameter. 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 omega(ln) 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 lambda and omega(ln), the superconducting critical temperatureis 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.