Triply degenerate topological phase and stretchable Fermi arc surface states in gyromagnetic metamaterials

Triple-fold band degeneracy (TBD) is an intriguing phase of topological semimetals which appears as the intermediate state between the four-folded degenerated Dirac points and the two-folded Weyl points. The resemblance of TBD in the photonics is interesting, because it indicates nonzero Berry curvature in momentum space and nontrivial topological property in real space. Recently, it was reported that TBD could be realized in the classical wave systems including phononic and photonic crystals. Unfortunately, those periodic structures can hardly provide a systematic strategy nor a compact layout in practical implementations. Hence, the resemblance of TBD is still a big challenge in topological photonics. In this work, we demonstrate that homogeneous gyromagnetic metamaterials (GMs) can be a good framework to stimulate the peculiar TBD. We discuss the emulation of triple degeneracy in dispersive GMs by carefully tuning the constitutive parameters. The introduction of nonlocality in the constitutive parameter of GMs provides the freedom of topology control of the GMs. Further, Fermi arc surface states are discussed and shown to be reflectionless against sharp corners. Remarkably, Fermi arc surface states, which occur at the boundary between the vacuum and the GMs, can be stretchable by tailoring the gap width of the GM's band structure. Our work provides a practical and flexible route to resemble TBD, which is of fundamental importance in designing reflectionless and unidirectional photonic topological devices.