Nonlinear topological Toda quasicrystal

TL;DR

This paper explores the effects of nonlinearity on topological edge states in a quasicrystal modeled by a generalized Toda lattice with irrational periodic modulations, revealing their robustness and inducing a localization transition.

Contribution

It introduces a nonlinear topological quasicrystal model based on the Toda lattice with irrational modulated hoppings, demonstrating the survival of edge states and a new localization transition.

Findings

Topological edge states persist under nonlinearity.

An extended-localization transition is induced by hopping modulation.

The model is experimentally realizable with transmission line circuits.

Abstract

Topological edge states are known to emerge in certain quasicrystals. We investigate a topological quasicrystal in the presence of nonlinearity by generalizing the Toda lattice to include modulated periodic hoppings, where the period is taken irrational to the original lattice. It is found that topological edge states in a quasicrystal survive against nonlinearity based on the quench dynamics. It is also found that an extended-localization transition is induced by the quasicrystal hopping modulation. The present model is experimentally realizable by a transmission line with variable capacitance diodes, where the inductance is modulated.