Anisotropic nonlinear optical response of nodal-loop materials

Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the three-dimensional Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. In this paper, we investigate the semiclassical optical response of two nodal loops in linked, unlinked, and touching configurations, focusing particularly on the interplay of response anisotropy and nonlinearity. We provide a geometric picture that unifies these aspects and sheds light on the effects of nodal topology and geometry. Based on a model abstracted from generic multi-nodal-loop scenarios, both with or without linkages, our findings will be applicable for a large class of nodal semimetal materials with multiple nodal lines or loops.