Electronic structure of noncentrosymmetric B20 compound HfSn and tuning of multifold band-crossing points

We present a detailed theoretical study of the electronic structure of hafnium tin HfSn crystallizing in a $\mathrm{B}20$ structure, renowned for the diversity of physical and peculiar topological properties. The chiral crystal structure of these materials protects multifold band crossings located at high-symmetry points. We employ density functional methods to reveal basic features of the band structure and Fermi surface topology of HfSn, on top of which a tight-binding model is built. The compound exhibits a fourfold band crossing pinned at the $\mathrm{\Gamma }$ point. We investigate routes that can shift such crossings towards the Fermi level, offering a way to possibly tune the compound's properties. Specifically, we show that the energy position of the fourfold crossing can be easily manipulated via external perturbations such as strain and pressure. Considering that this point carries a topological charge larger than 1, such tuning is of great importance. We anticipate that the approach presented in the current study can be utilized to investigate symmetry-protected crossings in a wide class of materials.