Superdiffusive transport on lattices with nodal impurities

It is well known that in the 1D Anderson model, the system is always localized, regardless of how small the disorder strength is. Here, the authors demonstrate that by replacing the standard onsite disorder term, ${\ensuremath{\sum}}_{i}{ϵ}_{i}\phantom{\rule{0}{0ex}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}\phantom{\rule{0}{0ex}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}}_{i}$, with a nodal disorder term, ${\ensuremath{\sum}}_{i}{ϵ}_{i}\phantom{\rule{0}{0ex}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{d}}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}\phantom{\rule{0}{0ex}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{d}}_{i}$, where ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{d}}_{i}={\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}}_{i}+i\phantom{\rule{0}{0ex}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}}_{i+1}$, the system becomes superdiffusive. The nodal disorder introduces a node in momentum space, resulting in a divergence of the localization length at the nodal momentum. This divergence in localization length induces superdiffusive transport.