Electrons and phonons in the ternary alloy CaAl_2−xSi_x as a function of composition

We report a detailed first-principles study of the structural, electronic, and vibrational properties of the superconducting C₃₂ phase of the ternary alloy CaAl_2−xSi_x, both in the experimental range 0.6⩽x⩽1.2, for which the alloy has been synthesized, and in the theoretical limits of high aluminum and high silicon concentration. Our results indicate that, in the experimental range, the dependence of the electronic bands on composition is well described by a rigid-band model, which breaks down outside this range. Such a breakdown, in the (theoretical) limit of high aluminum concentration, is connected to the appearance of vibrational instabilities and results in important differences between CaAl₂ and MgB₂. Unlike MgB₂, the interlayer band and the out-of-plane phonons play a major role on the stability and superconductivity of CaAlSi and related C₃₂ intermetallic compounds.