Topology and Localizations in a 2D Su-Schrieffer-Heeger Model with Domain Walls, Quasi-periodic Disorder and Periodic Hopping Modulations

Abstract

A two dimensional (2D) Su-Schrieffer-Heeger (SSH) model with topological defects like domain walls (DW) / vortices or quasi-periodic disorders is a perfect blend for investigating topology and localization of quantum states. In a 2D SSH model, zero energy states (ZES) lie within the dispersion continuum for both periodic and open boundaries. We consider two different distribution of DWs of which the first one shows the bound states in continuum (BIC) to populate at the corners (producing higher order topological modes) or the DW center while the second one, with a vortex like radially symmetric distribution of hopping modulations, shows localizations along the DWs and the edges. The topological yet gapped in-gap states, with nonzero Zak phases, show an opposite trend with localizations at the edges and along the DWs in the first case as opposed to localizations at the DW center in the second case. Investigation on the effect of on-site quasiperiodic disorders manifests the usual tendency of the states to localize. However, reentrant localization behavior is also captured for judicious choice of the disordered term, making this the first reported example of its kind in a 2D system. Furthermore, while varying the hopping periodicity, we discover that anisotropic hopping modulations along x and y directions within the lattice produces significant changes in topological features where bulk ZES get exhausted leaving only topological boundary modes at zero energies. We also discuss the fate of these states in presence of the DWs. All these analysis depicting topological/localization features of varied kinds can become very useful in the field of quantum computation and information processing.