Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study

Surface states of the Fibonacci chain are studied within the tight binding off-site model for clusters and approximants by numerical and transfer matrix methods. In each gap of the bulk spectrum a surface state can exist. The existence and energy of a surface state depend on the boundary conditions at the surface. The exponential envelope of surface states is used to define a localization length, which is shown to depend only on the energy of a specific state.