---
_id: '61255'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Topological states
    have been widely investigated in different types of systems and lattices. In the
    present work, we report on topological edge states in double-wave (DW) chains,
    which can be described by a generalized Aubry-André-Harper (AAH) model. For the
    specific system of a driven-dissipative exciton polariton system we show that
    in such potential chains, different types of edge states can form. For resonant
    optical excitation, we further find that the optical nonlinearity leads to a multistability
    of different edge states. This includes topologically protected edge states evolved
    directly from individual linear eigenstates as well as additional edge states
    that originate from nonlinearity-induced localization of bulk states. Extending
    the system into two dimensions (2D) by stacking horizontal DW chains in the vertical
    direction, we also create 2D multi-wave lattices. In such 2D lattices multiple
    Su–Schrieffer–Heeger (SSH) chains appear along the vertical direction. The combination
    of DW chains in the horizonal and SSH chains in the vertical direction then results
    in the formation of higher-order topological insulator corner states. Multistable
    corner states emerge in the nonlinear regime.</jats:p>"
author:
- first_name: Tobias
  full_name: Schneider, Tobias
  last_name: Schneider
- first_name: Wenlong
  full_name: Gao, Wenlong
  id: '78853'
  last_name: Gao
- first_name: Thomas
  full_name: Zentgraf, Thomas
  id: '30525'
  last_name: Zentgraf
  orcid: 0000-0002-8662-1101
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
- first_name: Xuekai
  full_name: Ma, Xuekai
  id: '59416'
  last_name: Ma
citation:
  ama: Schneider T, Gao W, Zentgraf T, Schumacher S, Ma X. Topological edge and corner
    states in coupled wave lattices in nonlinear polariton condensates. <i>Nanophotonics</i>.
    2024;13(4):509-518. doi:<a href="https://doi.org/10.1515/nanoph-2023-0556">10.1515/nanoph-2023-0556</a>
  apa: Schneider, T., Gao, W., Zentgraf, T., Schumacher, S., &#38; Ma, X. (2024).
    Topological edge and corner states in coupled wave lattices in nonlinear polariton
    condensates. <i>Nanophotonics</i>, <i>13</i>(4), 509–518. <a href="https://doi.org/10.1515/nanoph-2023-0556">https://doi.org/10.1515/nanoph-2023-0556</a>
  bibtex: '@article{Schneider_Gao_Zentgraf_Schumacher_Ma_2024, title={Topological
    edge and corner states in coupled wave lattices in nonlinear polariton condensates},
    volume={13}, DOI={<a href="https://doi.org/10.1515/nanoph-2023-0556">10.1515/nanoph-2023-0556</a>},
    number={4}, journal={Nanophotonics}, publisher={Walter de Gruyter GmbH}, author={Schneider,
    Tobias and Gao, Wenlong and Zentgraf, Thomas and Schumacher, Stefan and Ma, Xuekai},
    year={2024}, pages={509–518} }'
  chicago: 'Schneider, Tobias, Wenlong Gao, Thomas Zentgraf, Stefan Schumacher, and
    Xuekai Ma. “Topological Edge and Corner States in Coupled Wave Lattices in Nonlinear
    Polariton Condensates.” <i>Nanophotonics</i> 13, no. 4 (2024): 509–18. <a href="https://doi.org/10.1515/nanoph-2023-0556">https://doi.org/10.1515/nanoph-2023-0556</a>.'
  ieee: 'T. Schneider, W. Gao, T. Zentgraf, S. Schumacher, and X. Ma, “Topological
    edge and corner states in coupled wave lattices in nonlinear polariton condensates,”
    <i>Nanophotonics</i>, vol. 13, no. 4, pp. 509–518, 2024, doi: <a href="https://doi.org/10.1515/nanoph-2023-0556">10.1515/nanoph-2023-0556</a>.'
  mla: Schneider, Tobias, et al. “Topological Edge and Corner States in Coupled Wave
    Lattices in Nonlinear Polariton Condensates.” <i>Nanophotonics</i>, vol. 13, no.
    4, Walter de Gruyter GmbH, 2024, pp. 509–18, doi:<a href="https://doi.org/10.1515/nanoph-2023-0556">10.1515/nanoph-2023-0556</a>.
  short: T. Schneider, W. Gao, T. Zentgraf, S. Schumacher, X. Ma, Nanophotonics 13
    (2024) 509–518.
date_created: 2025-09-12T11:19:22Z
date_updated: 2025-09-12T11:22:41Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '705'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '27'
doi: 10.1515/nanoph-2023-0556
intvolume: '        13'
issue: '4'
language:
- iso: eng
page: 509-518
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '54'
  name: TRR 142 - Project Area A
- _id: '55'
  name: TRR 142 - Project Area B
- _id: '61'
  name: 'TRR 142; TP A04: Nichtlineare Quantenprozesstomographie und Photonik mit
    Polaritonen in Mikrokavitäten'
- _id: '170'
  name: 'TRR 142; TP B09: Effiziente Erzeugung mit maßgeschneiderter optischer Phaselage
    der zweiten Harmonischen mittels Quasi-gebundener Zustände in GaAs Metaoberflächen'
publication: Nanophotonics
publication_identifier:
  issn:
  - 2192-8614
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: Topological edge and corner states in coupled wave lattices in nonlinear polariton
  condensates
type: journal_article
user_id: '16199'
volume: 13
year: '2024'
...