The effect of staggered nonlinearity on the Su-Schrieffer-Heeger model

TL;DR

This paper explores how sublattice-dependent nonlinearity affects the topological properties of the SSH model, revealing phase transitions and edge states through analytical and numerical methods.

Contribution

It introduces a nonlinear Zak phase and demonstrates nonlinear-induced topological phase transitions in the SSH model.

Findings

High nonlinearity causes a topological phase transition with Zak phase discontinuity.

Edge states have energy independent of nonlinear parameters.

Persistent band touching points similar to Weyl points are observed.

Abstract

We investigate the spectral properties of the Su-Schrieffer-Heeger (SSH) model with sublattice-dependent onsite nonlinearity. Two complementary approaches are employed in our studies. First, Bloch state solutions under periodic boundary conditions are assumed to enable semi-analytical treatment, which allows us to obtain the system's energy band structure and further derive a general expression of the Zak phase that incorporates nonlinearity-induced correction (referred to as nonlinear Zak phase). This analysis reveals that, at sufficiently high nonlinearities, a nonlinearity-induced topological phase transition occurs, marked by a discontinuity in the nonlinear Zak phase. The second approach amounts to numerically obtaining other (non-Bloch) solutions under open boundary conditions, employing the Self-Consistent Field Iterative Method. Its main results include the observation of an edge state's energy that is independent of a nonlinear parameter, a persisting band touching point that only shifts in the presence of perturbations reminiscent of Weyl points in a Weyl semimetal, as well as delocalized solutions that persist even at extreme nonlinearity strengths. These findings illuminate the rich interplay between topology and nonlinearity in lattice models with potential realization in optical/acoustic waveguide settings.