# Interface states in polariton topological insulators

## TL;DR

This paper explores the properties of topological interface states in polariton condensates within honeycomb and Lieb arrays, highlighting their tunability, topological protection, and nonlinear behaviors such as soliton formation and bistability.

## Contribution

It introduces the concept of interface states arising from overlapping topological gaps in coupled arrays, and analyzes their properties, nonlinear dynamics, and robustness in polariton topological insulators.

## Key findings

- Interface states depend on the overlap of topological gaps and their Chern number differences.
- Wide tuning of power concentration between Lieb and honeycomb arrays is possible.
- Topological protection prevents backscattering and supports stable nonlinear states.

## Abstract

We address linear and nonlinear topological interface states in polariton condensates excited at the interface of the honeycomb and Lieb arrays of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. Such interface states appear only in total energy gaps of the composite structure when parameters of the honeycomb and Lieb arrays are selected such that some topological gaps in the spectrum of one of the arrays overlap with topological or nontopological gaps in the spectrum of the other array. This is in contrast to conventional edge states at the interface of periodic topological and uniform trivial insulators, whose behavior is determined exclusively by the spectrum of the topological medium. The number of emerging interface states is determined by the difference of the Chern numbers of the overlapping gaps. Illustrative examples with one or two coexisting unidirectional interface states are provided. The representative feature of the system is the possibility of wide tuning of the concentration of power of the interface states between two limiting cases when practically all power is concentrated either in the Lieb or the honeycomb array. Localization of the interface states and their penetration depth into arrays drastically vary with Bloch momentum or upon modification of the amplitude of the interface state in the nonlinear regime. We illustrate topological protection of the interface states manifested in the absence of backscattering on interface defects, and study their modulation instability in the nonlinear regime. The latter leads to formation of quasisolitons whose penetration into different arrays also depends on Bloch momentum. In addition, we discuss the impact of losses and coherent pump leading to bistability of the interface states.

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Source: https://tomesphere.com/paper/1905.09769