RESUMEN
Phonons play a crucial role in many properties of solid-state systems, and it is expected that topological phonons may lead to rich and unconventional physics. On the basis of the existing phonon materials databases, we have compiled a catalog of topological phonon bands for more than 10,000 three-dimensional crystalline materials. Using topological quantum chemistry, we calculated the band representations, compatibility relations, and band topologies of each isolated set of phonon bands for the materials in the phonon databases. Additionally, we calculated the real-space invariants for all the topologically trivial bands and classified them as atomic or obstructed atomic bands. We have selected more than 1000 "ideal" nontrivial phonon materials to motivate future experiments. The datasets were used to build the Topological Phonon Database.
RESUMEN
Time Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite the numerous demonstrations of 2D topological phases, few examples of 3D topological systems with TRS breaking exist. In this article, we devise a general strategy to design 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRS broken environment with orientable and arbitrarily large Chern vectors. The designs display topologically protected chiral and unidirectional surface states with disjoint equifrequency loops. The resulting crystals present the following characteristics: First, by increasing the Chern number, multiple surface states channels can be supported. Second, the Chern vector can be oriented along any direction simply changing the magnetization axis, opening up larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, by lowering the TRS breaking requirements, the system is ideal for realistic photonic applications where the magnetic response is weak.