EXTENDED STATES IN APERIODIC SYSTEMS

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