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Corner states in photonic higher-order Dirac semimetals

José A. Medina-Vázquez*, Evelyn Y. González-Ramírez, and José G. Murillo-Ramírez

  • Centro de Investigación en Materiales Avanzados S.C, Complejo Industrial Chihuahua, Miguel de Cervantes 120, C.P. 31136, Chihuahua, México

  • *Corresponding author: jose.medina@cimav.edu.mx
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Phys. Rev. A 107, 053511 – Published 12 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.053511

Abstract

The introduction of higher-order topological insulators featuring topological corner states has been an extremely active topic for the generation of confined modes. Recent studies show that corner states are not an exclusive feature of topological insulators but can also exist as bound states in the continuum (BIC). This suggests that corner states may exist in different topological phases that exhibit a higher-order character, beyond the conventional bulk-edge correspondence. In this paper, we show that corner states can appear in a higher-order Dirac semimetal phase of a two-dimensional photonic lattice. Such a lattice displays a dispersion relationship with a fourfold degeneracy, which serves to induce a higher-order topological phase transition, leaving a Dirac point between two edge bands. Just as Dirac modes exist in regular lattice defects, the nonconventional bulk-edge-corner correspondence leads to corner states in the Dirac semimetal phase. Notably, the induced corner state exhibits an algebraic decay characteristic of long-range interactions, predicted by the massless Dirac equation. The analysis of the field profile and quality factors indicates that the state is not a BIC, but rather a corner-Dirac state. We show that if the photonic lattice does not present a higher-order phase transition the existence of the corner-Dirac state does not arise. The results obtained in this paper indicate that corner states can exist throughout the entire topological phase transition process, even in the semimetal phase, and pave the way to generate light-matter interactions with such a photonic bath.

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Outline

Information

Phys. Rev. A 107, 053511– Published 12 May, 2023
  • Received 22 December 2022
  • Revised 9 April 2023
  • Accepted 1 May 2023
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