Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems

Understand

Weyl points in three spatial dimensions are characterized by a $\mathbb{Z}$-valued charge -- the Chern number -- which makes them stable against a wide range of perturbations.

• A set of Weyl points can mutually annihilate only if their net charge vanishes, a property we refer to as robustness.
• While nodal loops are usually not robust in this sense, it has recently been shown using homotopy arguments that in the centrosymmetric extension of the $\textrm{AI}$ symmetry class they nevertheless develop a $\mathbb{Z}_2$ charge analogous to the Chern number.
• Nodal loops carrying a non-trivial value of this $\mathbb{Z}_2$ charge are robust, i.e.