Localized states at zigzag edges of multilayer graphene and graphite stepsEduardo V. Castro1, N. M. R. Peres2 and J. M. B. Lopes dos Santos1
1 CFP and Departamento de Física, Faculdade de Ciências Universidade do Porto - P-4169-007 Porto, Portugal, EU
2 Center of Physics and Departamento de Física, Universidade do Minho - P-4710-057 Braga, Portugal, EU
received 18 July 2008; accepted in final form 13 August 2008; published October 2008
published online 1 September 2008
We report the existence of zero-energy surface states localized at zigzag edges of N-layer graphene. Working within the tight-binding approximation, and using the simplest nearest-neighbor model, we derive the analytic solution for the wave functions of these peculiar surface states. It is shown that zero-energy edge states in multilayer graphene can be divided into three families: i) states living only on a single plane, equivalent to surface states in monolayer graphene; ii) states with finite amplitude over the two last, or the two first layers of the stack, equivalent to surface states in bilayer graphene; iii) states with finite amplitude over three consecutive layers. Multilayer graphene edge states are shown to be robust to the inclusion of the next-nearest-neighbor interlayer hopping. We generalize the edge state solution to the case of graphite steps with zigzag edges, and show that edge states measured through scanning tunneling microscopy and spectroscopy of graphite steps belong to family i) or ii) mentioned above, depending on the way the top layer is cut.
73.20.-r - Electron states at surfaces and interfaces.
73.20.At - Surface states, band structure, electron density of states.
73.21.Ac - Multilayers.
© EPLA 2008