Edge states in honeycomb structures
James Lee -Thorp, CIMS

We present recent results on edge states in 2D honeycomb structures, such graphene and its photonic analogues. Edge states are modes which propagate parallel to a line-defect or edge, and are localized transverse to it. Certain edge states are topologically protected; they are stable against localized (even large) perturbations. We begin with a review of the properties of waves in continuous honeycomb structures, before outlining a bifurcation theory of topologically protected edge states. We will focus on a Schroedinger (electronic) model, but will also briefly discuss analogous results in the Maxwell (photonic) setting.