Quantum geometry and low-frequency optical conductivity of nodal planes

Nodal planes, two-dimensional symmetry-enforced band crossings, can carry a topological charge, similar to Weyl points. While the transport properties of Weyl points are well understood, those of nodal planes remain largely unexplored. These properties are influenced not only by the Berry curvature, but also by other quantum geometric quantities. In this work we study the quantum geometry - specifically the Berry curvature and quantum metric - and the linear optical conductivity of topological nodal planes. We introduce a low-energy model and investigate its low-frequency optical responses to determine the unique signatures of nodal planes. By comparing these findings to the optical response in a tight-binding model with a topological nodal plane, we observe consistent low-frequency behavior with a cubic power law. This paves the way for the experimental detection of nodal planes through optical conductivity measurements for which we suggest suitable materials, most promisingly the material group $X$Mo$_3$S$_3$ ($X$ = Rb, K, Cs).