Insights into electron and phonon topology: multi-fold fermions and Dirac nodal-line net bosons in SiX2 (X=P and As)

There has been a notable increase in enthusiasm for delving into new (quasi) particles within the domains of condensed matter and materials. Particularly, a distinctive excitement has arisen over a recently theorized exotic excitation found in a three-dimensional material, showcasing linear dispersion and the possibility of multi-fold degeneracy. In this article, we embark on an extensive investigation into the multi-fold degenerate exotic fermions beyond Dirac and Weyl in the pyrite-structured SiX2 compounds (with X as P and As). We delve into the topological attributes of band-touching nodes in fermions, featuring four- and six-fold degeneracy positioned at the Gamma and R points in the first Brillouin zone, analyzing them through symmetry analysis. Regarding bosons, employing symmetry analysis, this study identifies distinctive properties where three-nodal surfaces (NSs) and phononic Dirac nodal-line (DNL) nets coexist. These phononic DNL nets comprise three phononic DNLs that share a common nodal point in momentum space, positioned at the intersection of two out of the three k(i) planes (i = x, y, z). The presence of observable phononic surface states in these materials may facilitate their experimental detection, suggesting these materials' potential as prime candidates for realizing such phononic states in solid-state materials. Our investigation highlights the pyrite-structured SiX2 as a promising platform for studying multi-fold fermions and delving into their potential applications.