Extended states in one-dimensional aperiodic lattices with linearly varying patches

We introduce a family of one-dimensional aperiodic tight-binding models with linearly varying patches of A-type sites with on-site energies EA = 0 connected by single B-type sites with EB = W. We analytically show such structures have strong spatial correlations. We theoretically find states are extended at resonance levels in the vicinity of EM = -2 cos M if they are allowed energies, where M = md are the size differences of patches, d is the variation rate of patch sizes, m is an element of N+, and K = 1, 2, ... , M - 1. Related delocalization-localization transitions are explored. Numerical evidence is in excellent quantitative agreement with theoretical predictions.