  Controlling light propagation using artificial photonic crystals and
electromagnetic metamaterials is an important topic in the vibrant field of
photonics. Notably, chiral edge states on the surface or at the interface of
photonic Chern insulators can be used to make reflection-free waveguides. Here,
by both theoretical analysis and electromagnetic simulations, we demonstrate
that gyromagnetic hyperbolic metamaterials (GHM) are photonic Chern insulators
with superior properties. As a novel mechanism, the simultaneous occurrence of
the hyperbolic and gyromagnetic effects in these metamaterials is shown to open
the large topological band gaps with gap Chern number of one. Importantly,
unlike many other photonic Chern insulators, the GHM Chern insulators possess
non-radiative chiral edge modes on their surfaces, and thus allow to fabricate
unidirectional waveguides without cladding metals which generally incurr
considerable Ohmic loss. Furthermore, the photonic edge states in the proposed
Chern insulators are robust against disorder on a wide range of length scales,
in strong contrast to crystalline topological insulators, and the light flow
direction on the surface of the Chern insulators can be easily flipped by
switching the direction of an applied magnetic field. Fascinatingly, we find
that negative refraction of the topological surface wave occurs at the boundary
between the GHMs with the opposite signs of gyromagnetic parameters. Finally,
we show that compared with other photonic topological materials such as chiral
hyperbolic materials, the present GHM Chern insulators can be much easier to
fabricate.
