Extension of the hopping range in incommensurate systems can generate localised states

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Abstract
The effect of hopping beyond nearest neighbours on the electronic properties of incommensurate systems is discussed very little in the literature even though for example structural phase transitions from commensurate to incommensurate systems are impossible without interactions beyond nearest neighbours. The authors show here that extending the range of hopping in the well known Aubry model to include next-nearest-neighbour hopping gives rise to localised states in regions where the original model with only nearest-neighbour hopping gives all states extended. A short discussion of the relation of this result to the Aubry duality and the Soukoulis-Economou model is given.