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Time Reversal Symmetry (TRS) broken topological phases provide gaplesssurface states protected by topology, regardless of additional internalsymmetries, spin or valley degrees of freedom. Despite the numerousdemonstrations of 2D topological phases, few examples of 3D topological systemswith TRS breaking exist. In this article, we devise a general strategy todesign 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRSbroken environment with orientable and arbitrarly large Chern vectors. Thedesigns display topologically protected chiral and unidirectional surfacestates with disjoint equifrequency loops. The resulting crystals present thefollowing novel characteristics: First, by increasing the Chern number,multiple surface states channels can be supported. Second, the Chern vector canbe oriented along any direction simply changing the magnetization axis, openingup larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, bylowering the TRS breaking requirements, the system is ideal for realisticphotonic applications where the magnetic response is weak.

Cubic 3D Chern photonic insulators with orientable large Chern vectors