Modulation of a 3D Chern photonic crystal by means of Group Theory*

This work supports the computational investigation of a 3D Chern photonic crystal insulator engineered to host orientable, large Chern triplets, by Devescovi et al (see reference), with an analytical model based on Group Theory.

The application of an external magnetic field creates a Weyl dipole that is gapped by a real-space cell modulation that couples the points. We develop a general expansion of the energy bands around a given wavevector respecting the crystal symmetries. First, we model the splitting of the degeneracy by the magnetic field giving to the Weyl points. Then, we describe their gapping into a non-trivial insulating phase. The results facilitate the design of the structure by predicting properties of the system before any time-consuming numerical computation and allows the identification of the residual symmetries as the phase transitions occur. In particular, it correctly identifies what kinds of modulations will gap the dipole based on their symmetry properties and reproduces some topological features of the energy bands such as the chirality of the nodal points.