In the present investigation, based on density functional theory computational approach, we show how the experimentally accepted ${\mathrm{AlB}}_2$-like structure of the $\mathrm{SrAlGe}$ compound is suggested to be dynamically unstable at 0 K. We propose a stable configuration that is deduced from the detailed analysis of the phonon spectrum with a doubled unit cell and buckled $\mathrm{AlGe}$ layers. It allows to closely reproduce the experimental critical superconducting temperature assuming a phonon mediated superconductivity as described within BCS theory. A soft puckering mode is identified both as the cause for the structural instability and as the main contributor in the electron-phonon coupling constant. From the detailed study of the electronic structure, we show how a peierls-like distortion with the crystal symmetry lowering, affecting mainly the Al-$p_z$ orbitals, is correlated with the puckering and with the electron-phonon coupling mechanism.

在目前的研究中，我们基于密度泛函理论的计算方法，展示了如何在实验上接受 ${\mathrm{铝}}_{\mathrm{2个}}$的类似结构 $\mathrm{铝锗}$ 建议该化合物在0 K时是动态不稳定的。我们提出了一种稳定的构型，该构型是通过对声子谱进行了详细分析得出的，该声子谱具有双倍的晶胞和弯曲 $\mathrm{铝锗}$层。假设声子介导的超导性如BCS理论中所述，它可以紧密地再现实验临界超导温度。软起皱模式既被认为是结构不稳定性的原因，也是电子-声子耦合常数的主要贡献者。通过对电子结构的详细研究，我们显示出晶体对称性降低的类皮尔形畸变如何主要影响Al-$p_{ž}$ 轨道与褶皱和电子-声子耦合机制相关。