We study numerically the electronic properties of one-dimensional systems with long-range correlated binary potentials. The potentials are mapped from binary sequences with a power-law power spectrum over the entire frequency range, which is characterized by correlation exponent β. We find the localization length ξ increases with β. At system sizes N → ∞, there are no extended states. However, there exists a transition at a threshold βc. When β > βc, we obtain ξ > 0. On the other hand, at finite system sizes, ξ ≥ N may happen at certain β, which makes the system "metallic", and the upper-bound system size N*(β) is given.
