We examine the role of strong nonlinearity on topologically-robust edge state in a one-dimensional system. consider chain inspired from Su-Schrieffer-Heeger model, but with finite-frequency and dynamics governed by second-order differential equations. introduce cubic onsite-nonlinearity study this nonlinear effect state's frequency linear stability. Nonlinear continuation reveals that loses its...

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for integer quantum Hall transition. In addition to weak topological insulator phase already accommodated by framework in preexisting literature, our hosts strong phases. unambiguously demonstrate that phases emerge as intermediate between trivial and phase. Additionally, we fou...

A topological index is a characteristic value which represents some structural properties of chemical graph. We study strong double graphs and their generalization to compute Zagreb indices coindices. provide explicit computing formulas along with an algorithm generate verify the results. also find relation between these indices. 3D graphical representation are presented understand dynamics afo...

We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological "Anderson" insulator, a new topological phase of quantum matter in three dimensions characterized by disordered insulating bulk and topologically protected conducting surface states.

Electron correlations amplify quantum fluctuations and, as such, they have been recognized the origin of a rich landscape phases. Whether and how lead to gapless topological states is an outstanding question, framework that allows for determining novel phases identifying new materials in pressing need. Here we advance general approach, which strong cooperate with crystalline symmetry drive stat...