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.
This is joint work with Charles
Fefferman (Princeton) and Michael Weinstein (Columbia).