Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.

We investigate the possibility of realizing quantum anomalous Hall effect in graphene. We show that a bulk energy gap can be opened in the presence of both Rashba spin-orbit coupling and an exchange field. We calculate the Berry curvature distribution and find a non-zero Chern number for the valence bands and demonstrate the existence of gapless edge states. Inspired by this finding, we also study, by first principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result.

Topological insulators can exhibit strong magneto-electric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low frequencies θF=tan(-1)α, where α is the vacuum fine structure constant, and that it has a giant Kerr rotation θK=π/2. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall conductivity of a topological insulator's helical quasiparticles.

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.

We present a theory of the magneto-optical Faraday and Kerr effects of topological insulator (TI) films. For film thicknesses short compared to wavelength, we find that the low-frequency Faraday effect in ideal systems is quantized at integer multiples of the fine structure constant, and that the Kerr effect exhibits a giant π/2 rotation for either normal or oblique incidence. For thick films that contain an integer number of half wavelengths, we find that the Faraday and Kerr effects are both quantized at integer multiples of the fine structure constant. For TI films with bulk parallel conduction, we obtain a criterion for the observability of surface-dominated magneto-optical effects. For thin samples supported by a substrate, we find that the universal Faraday and Kerr effects are present when the substrate is thin compared to the optical wavelength or when the frequency matches a thick-substrate cavity resonance. Our theory applies equally well to any system with two conducting layers that exhibit quantum Hall effects.