Symmetry-breaking bifurcation of coupled topological edge states

TL;DR

This paper demonstrates that symmetry-breaking bifurcations in coupled topological edge states can be used to induce spontaneous symmetry breaking in nonlinear topological lattices, with potential applications in controlling topological states.

Contribution

It introduces a universal mechanism for spontaneous symmetry breaking in nonlinear topological systems via symmetry-breaking bifurcations of coupled edge states.

Findings

Supercritical bifurcation of symmetric CTESs with increasing nonlinearity

Formation of stable asymmetric states beyond critical threshold

Expansion of stable CTES frequency range with increased interchain coupling

Abstract

We propose that the symmetry-breaking bifurcation of coupled topological edge states (CTESs) can be used as a general principle for achieving spontaneous symmetry breaking (SSB) in a nonlinear topological lattice. Using an optical resonator array composed of two Su-Schrieffer-Heeger (SSH) chains as an example, we find that as the nonlinearity strength increases, the symmetric CTESs undergo a supercritical bifurcation. Beyond the critical threshold, the originally stable symmetric state becomes unstable, leading to the formation of a pair of stable asymmetric states. Both sides of the symmetric CTESs exhibit sublattice polarization, while the side of the asymmetric CTESs that is predominantly occupied demonstrates stronger sublattice polarization. We further find that as interchain coupling increases, the frequency range for stable CTESs expands, while the frequency range for stable asymmetric CTESs decreases. Our work provides a universal mechanism for realizing SSB in nonlinear topological lattices.