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We introduce a family of 1D aperiodic tight-binding models with linearlyvarying patches of A-type sites with on-site energies $\epsilon_A=0$ connectedby single B-type sites with $\epsilon_B=W$. We analytically show suchstructures have strong spatial correlations. We theoretically find states areextended at resonance levels in the vicinity of$E^\kappa_M=-2\cos\frac{\kappa\pi}{M}$ if they are allowed energies, where$M=md$ are the size differences of patches, $d$ is the variation rate of patchsizes, $m\in \mathcal{N_{+}}$ and $\kappa=1,2,\cdots,M-1$. Relateddelocalization-localization transitions are explored. Numerical evidences arein excellent quantitative agreement with theoretical predictions.

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