Abstract

The existence of electronic states in aperiodic chains-both the generalized Fibonacci (GF) chain with the inflation rule (A to AmBn, B to A) and the generalized Thue-Morse (GTM) (A to AmBn, B to BnAm) chain-is proved analytically. There might be a critical value lambda c, for the GF chain. If the ratio VA/VB is greater than lambda c, where VA and VB are the potentials in the GF hopping Hamiltonian, our numerical calculation seems to show that the extended state will vanish.

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