# Non-linear second-order topological insulators

## TL;DR

This paper introduces non-linear second-order topological insulators whose topological states can be dynamically controlled by excitation intensity, enabling reconfigurable topological phases without structural modifications.

## Contribution

The work demonstrates the theoretical and experimental realization of non-linear second-order topological insulators with tunable topological states driven by non-linearity, a novel concept in topological physics.

## Key findings

- Edge and corner states can be induced by tuning excitation intensity.
- Topological phase transitions can be controlled externally without structural changes.
- Non-linear effects enable dynamic spectral tuning of topological states.

## Abstract

We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of non-linearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the excitation intensity. This allows global external control over topological phase transitions and switching to a phase with non-zero bulk polarization, without requiring any structural or geometrical changes. We further show how these non-linear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.

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Source: https://tomesphere.com/paper/1906.06605