Electrons and phonons in the ternary alloy CaAl$_{2-x}$Si$_x$} as a function of composition

TL;DR

This study uses first-principles calculations to analyze how the electronic, vibrational, and structural properties of the superconducting CaAl$_{2-x}$Si$_x$ alloy vary with composition, revealing the limits of a rigid-band model and the role of phonons in stability.

Contribution

It provides a detailed theoretical investigation of CaAl$_{2-x}$Si$_x$, highlighting the breakdown of the rigid-band model at high Al concentrations and the importance of phonons for superconductivity.

Findings

Rigid-band model describes electronic bands within experimental composition range.

Vibrational instabilities occur at high aluminium concentrations.

Interlayer band and out-of-plane phonons influence stability and superconductivity.

Abstract

We report a detailed first-principles study of the structural, electronic and vibrational properties of the superconducting C$_{32}$ phase of the ternary alloy CaAl$_{2-x}$Si$_x$, both in the experimental range $0.6 \leq x \leq 1.2$, for which the alloy has been synthesised, and in the theoretical limits of high aluminium 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 aluminium concentration, is connected to the appearance of vibrational instabilities, and results in important differences between CaAl$_2$ and MgB$_2$. Unlike MgB$_2$, the interlayer band and the out-of-plane phonons play a major role on the stability and superconductivity of CaAlSi and related C$_{32}$ intermetallic compounds.