We investigate the spectral function of Bloch states in a one-dimensional tight-binding noninteracting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel polynomial method, which has an O(N) computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, ∝|k| −α , we show that the spectral function is not self-averaging for α 1.

The possibility of having a delocalization transition in the 1D de Moura-Lyra class of models (having a power-spectrum ∝ q −α ) has been the object of a long standing discussion in the literature. In this paper, we report the first numerical evidences that such a transition happens at α = 1, where the localization length (measured from the scaling of the conductance) is shown to diverge as (1 − α) −1 . The persistent finite-size scaling of the data is shown to be caused by a very slow convergence of the nearest-neighbor correlator to its infinite-size limit, and controlled by the choice of a proper scaling parameter. Our results for these models are consistent with a localization of eigenstates that is driven by a persistent small-scale noise, which vanishes as α → 1 − . This interpretation in confirmed by analytical perturbative calculations which are built on previous work. Finally, the nature of the delocalization transition is discussed and the conclusions are illustrated by numerical work done in the α > 1 regime.

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The electronic structure of a cubic T -symmetric Weyl semimetal is analyzed in the presence of atomic-sized vacancy defects. Isolated vacancies are shown to generate nodal bound states with r −2 asymptotic tails, even when immersed in a weakly disordered environment. These states show up as a significantly enhanced nodal density of states which, as the concentration of defects is increased, reshapes into a nodal peak that is broadened by intervacancy hybridization into a comb of satellite resonances at finite energies. Our results establish point defects as a crucial source of elastic scattering that leads to nontrivial modifications in the electronic structure of Weyl semimetals.