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Robust Zero Modes in Non-Hermitian Systems without Global Symmetries

Jose D. H. Rivero, Courtney Fleming, Bingkun Qi, Liang Feng, and Li Ge
Phys. Rev. Lett. 131, 223801 – Published 29 November 2023
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    Abstract

    We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the “nucleus” that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the “zeroness” of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.

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    • Received 5 June 2023
    • Accepted 2 November 2023

    DOI:https://doi.org/10.1103/PhysRevLett.131.223801

    © 2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Physical Systems
    Microcavity & microdisk lasersNon-Hermitian systemsWaveguides
    Atomic, Molecular & Optical

    Authors & Affiliations

    Jose D. H. Rivero1,2, Courtney Fleming1,2, Bingkun Qi1,2, Liang Feng3, and Li Ge1,2

    • 1College of Staten Island, CUNY, Staten Island, New York 10314, USA
    • 2The Graduate Center, CUNY, New York, New York 10016, USA
    • 3Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

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    Issue

    Vol. 131, Iss. 22 — 1 December 2023

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    Images

    • Figure 1
      Figure 1

      Schematics of systems hosting an SFZM, where the boundary is a single cavity in (a) and a small cluster in (b).

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    • Figure 2
      Figure 2

      (a) Representative complex energy spectrum for the configuration shown in Fig. 1 with 30 bulk lattice sites. Both on-site energy and couplings in the bulk are uniformly distributed in [−g/2,g/2], whereas on-site loss is uniformly distributed in [−g/10,0]. Black and orange dots mark the SFZM and bulk nonzero modes. Black arrow shows the trajectory of the SFZM when the cavity loss in the boundary is gradually compensated by an increasing pump. (b) Spatial profiles of the SFZM and the circled bulk mode in (a). Shaded area shows the bulk.

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    • Figure 3
      Figure 3

      Same as Fig. 2 but with a three-site boundary and another arbitrary bulk. k=g, k′=−g, and q=2g are used.

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    • Figure 4
      Figure 4

      (a) Schematics of a breathing Kagome lattice, with the non-Hermitian boundary attached. (b),(c) Band diagram without and with the boundary. g=t=tb and 20 rows of cavities are used. (d) Symmetric higher-order corner state in the topological gap at ta/tb=0.4 without the boundary. (e),(f) The wave functions of the SFZMs at ta/tb=0.4, 2.5 [open and closed dots in (c)]. 10 rows of cavities are used in (d)–(f) for a compact illustration.

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    • Figure 5
      Figure 5

      (a) Wave function of a near-zero mode without the boundary and with disorder. On-site and coupling disorders are uniform in the ranges [−0.1,0.1]tb and [−0.4,0.4]tb, respectively. (b) Corresponding SFZM with the boundary at the top.

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