Anatomy

Physics

Pure mathematics

Mathematics

Mathematical physics

Massless particle

NODAL

Medicine

Physical review. B./Physical review. B

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

Complete classification of band nodal structures and massless excitations