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 or nodal lines can close into loops trace out intricate knotted linked configurations complicated topologies. In this paper, we investigate semiclassical optical response of two linked, unlinked, touching configurations, focusing particularly on interplay anisotropy nonlinearity. We provide a geometric picture that unifies these aspects sheds light effects topology geometry. Based model abstracted from generic multi-nodal-loop scenarios, both without linkages, our findings will be applicable for large class semimetal materials multiple loops.