Transforming the concept of band topology fostered in electron systems to electromagnetic waves opens a completely new direction for harnessing propagation of light. It is observed that electromagnetic modes in honeycomb photonic crystals exhibit Dirac-type frequency dispersions, which are accompanied by emergent spin degree of freedom, and that deforming the honeycomb structure in a designed way gives birth to a photonic analogue of quantum spin Hall effect. In this talk I will first show that the main physics can be captured phenomenologically by the k∙p theory, and discuss that the photonic topology can be characterized in terms of the Wilson loops based on the C_2 T symmetry. Then I will introduce examples to demonstrate how the recipe can be exploited for harnessing light and deriving advanced optic properties.

In this talk, I will present a new mechanism of impurity screening in quantum critical chains, where topological defect lines of the underlying conformal field theory provide the screening channels. This leads to exotic boundary states that go beyond Cardy’s types. As an example, we demonstrate impurity screening by defect in a spin-1 chain described by the SU(3)_1 WZW model, with numerical results for the spectrum and Affleck-Ludwig entropy matching the theoretical predictions.