2D Su-Schrieffer-Heeger Model with static domain walls and quasiperiodic disorder

We revisit the problem of a two dimensional Su-Schrieffer-Heeger (SSH) model on a square lattice to first minutely analyze its spectra including zero energy states (ZES) and in-gap states both under periodic and open boundaries. Thereafter, a series of antiphase domain walls (DW), distributed along two orthogonal lines, are introduced in the lattice with SSH like hoppings and this causes the ZES to localize not only at the corners but also at the intersection of the lines of domain walls. In-gap states not only populate at the edges but also show finite amplitudes along the DW lines. A different scenario appears for a radially symmetric distribution of domain walls along a circle around a poit within the lattice. It produces in-gap states localized at the center of the DW circle while the ZES show localizations around it in a symmetric fashion in the square lattice. We also probe the effect of a diagonal quasiperiodic disorder on the spectra and eigen-states of the 2D SSH model. This gives localization of the states more with a stronger disorder. We calculate participation ratios of the states and their averages to demonstrate how such localization develops with disorder. Lastly we also elaborate further on the eigenvalue and eigenstates of a few periodically hopping modulated cases, previously outlined briefly in the article: Jour. Phys. Cond.-Mat.{\bf 36}, 065301 (2024) and also give an account of the changed features of the spectra as a result of the application of DWs there. Our findings on these various fronts can increase many-fold the visibility of this popular model and the outcomes can be utilized in many emerging fields like topological quantum information processing, for example, by designing topological shielding of various kinds.