Complete classification of band nodal structures and massless excitations

Energy band nodal structures (nodal points/lines/surfaces) in the Brillouin zone (BZ) have received immense research interest past decade, while their complete classification is still lacking. Here, we focus on all 1651 magnetic space groups (MSGs) and 528 layer (MLGs) to provide a dataset of symmetry-diagonalizable strictly nearly emanating from nodes (BNs) at symmetric $k$ points. Using our dataset, one can quickly know $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ models. Based models, find that charge-4 Weyl point, thought only exist spinless setting before, spinful setting. Our also be applied identify associated structures, which composed several lines or/and surfaces given BN. In this way, are flexible but fixed point BZ. includes both settings with latter applicable for bosons like phonons electronic materials negligible spin-orbit coupling. We show same as BNs, especially surfaces, ubiquitous. Finally, predict hundreds ever-synthesized essential extended or material.