Graphene edge states in a tight binding model

Abstract: We study a standard tight binding model of graphene, sharply terminated along an edge. It is well known that zero energy (“flat band”) edge states arise for a "zigzag" edge, while an "armchair" edge gives rise to no edge states.

We present joint work with S. Fliss and M. Weinstein that determines which rational edges give rise to flat band edge states, and exhibits formulas for such edge states when they exist. The joint work includes also preliminary results on non-flat-band edge states.

Thanks to results presented in Michael Weinstein's lecture, flat bands for a tight binding model give rise to almost flat band edge states for a continuum model.

mathematical physicsanalysis of PDEsquantum physics

Audience: researchers in the topic

Mathematical Challenges in Quantum Mechanics 2021 Workshop