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arxiv: 2508.10901 · v3 · submitted 2025-08-14 · ❄️ cond-mat.mes-hall

Exceptional flat bands in bipartite non-Hermitian lattices

Juan Pablo Esparza , Vladimir Juri\v{c}i\'c This is my paper

Pith reviewed 2026-05-18 22:39 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords flat bandsnon-Hermitian latticesbipartite latticesexceptional pointsexceptional flat bandsdegeneracy mismatchbiorthogonal modes
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The pith

Non-Hermitian bipartite lattices support flat bands when one sublattice has higher degeneracy in its momentum-independent eigenvalue than the other.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the degeneracy-mismatch rule for flat bands in Hermitian bipartite lattices carries over unchanged to the non-Hermitian setting. Whenever one sublattice carries a momentum-independent eigenvalue whose degeneracy exceeds that of its partner, flat bands appear even in the presence of gain, loss, or complex couplings. At exceptional points the dispersive bands merge into exceptional flat bands whose eigenmodes are biorthogonal and span both sublattices. These states have energies and lifetimes that can be adjusted by sublattice asymmetry or non-reciprocal terms. The construction unifies flat-band formation across closed and open systems and points to dispersionless modes with no Hermitian counterpart.

Core claim

In bipartite non-Hermitian lattices, flat bands arise whenever one sublattice hosts a momentum-independent eigenvalue whose degeneracy exceeds that of the partner sublattice. At exceptional points the dispersive bands coalesce into exceptional flat bands that persist beyond the singularities, featuring biorthogonal eigenmodes that span both sublattices and whose energies and lifetimes are tunable by sublattice chemical potentials and non-reciprocal couplings.

What carries the argument

Sublattice degeneracy mismatch for a momentum-independent eigenvalue

Load-bearing premise

A momentum-independent eigenvalue on one sublattice remains exactly constant and keeps a strictly higher degeneracy than its partner even after arbitrary non-Hermitian perturbations are added.

What would settle it

Adding non-Hermitian couplings that render the higher-degeneracy eigenvalue momentum-dependent should eliminate the flat bands.

Figures

Figures reproduced from arXiv: 2508.10901 by Juan Pablo Esparza, Vladimir Juri\v{c}i\'c.

Figure 1
Figure 1. Figure 1: FIG. 1. Left: the square Lieb lattice with three inequivalent [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The diagonal element of the quantum metric in the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Energy spectrum of the tight-binding model for [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Two-dimensional non-Hermitian Lieb lattice. The [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

Flat bands, in which kinetic energy is quenched and quantum states become macroscopically degenerate, host a rich variety of correlated and topological phases, from unconventional superconductors to fractional Chern insulators. In Hermitian lattices, their formation mechanisms are now well understood, but whether such states persist, and acquire new features in non-Hermitian (NH) { crystals}, relevant to open and driven systems, has remained an open question. Here we show that the Hermitian principle for flat-band formation in bipartite lattices, based on a sublattice degeneracy mismatch, extends directly to the NH regime: whenever one sublattice hosts a momentum-independent eigenvalue with degeneracy exceeding that of its partner on the other sublattice, flat bands arise regardless of gain, loss, or complex couplings. Strikingly, at exceptional points, dispersive bands coalesce to form \emph{exceptional flat bands} (EFBs) that persist beyond these singularities, exhibiting biorthogonal eigenmodes spanning both sublattices, with energies and lifetimes tunable via sublattice asymmetry and non-reciprocal couplings. This general framework unifies Hermitian and NH flat-band constructions, and reveals dispersionless states with no closed-system analogue, as is the case of a bipartite lattice with imbalanced but constant sublattice chemical potentials. The proposed construction is applicable to synthetic platforms, from classical metamaterials, where flat bands can be directly emulated, to quantum-engineered systems such as photonic crystals and ultracold atom arrays, which should host correlated and topological phases emerging from such EFBs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript claims that the Hermitian principle for flat-band formation in bipartite lattices—based on a sublattice degeneracy mismatch—extends directly to the non-Hermitian regime. Whenever one sublattice hosts a momentum-independent eigenvalue whose degeneracy exceeds that of its partner, flat bands arise regardless of gain, loss, or complex couplings. The work further identifies exceptional flat bands (EFBs) that form at exceptional points, persist beyond them, and exhibit biorthogonal eigenmodes spanning both sublattices with tunable energies and lifetimes via sublattice asymmetry and non-reciprocal couplings. The construction is presented as unifying Hermitian and NH cases and applicable to synthetic platforms.

Significance. If the central extension holds, the result provides a parameter-free counting argument that unifies flat-band constructions across Hermitian and non-Hermitian settings and identifies dispersionless states without closed-system analogues (e.g., imbalanced constant sublattice chemical potentials). This could guide design of flat bands in open systems such as photonic crystals and metamaterials, with potential for correlated or topological phases.

major comments (1)
  1. [General framework / derivation following abstract] The load-bearing assumption that a momentum-independent eigenvalue on the majority sublattice remains exactly k-independent (and retains its algebraic multiplicity) after arbitrary non-Hermitian perturbations is not demonstrated for general block forms. In a general NH bipartite Hamiltonian the off-diagonal blocks carry complex momentum dependence; their product with the inverse of the minority block can feed k-dependent corrections back into the effective equation for the majority eigenvalue, shifting the root or reducing multiplicity. The manuscript must supply the explicit characteristic equation or block-diagonalization step showing that this feedback vanishes for arbitrary gain/loss and complex couplings (see the paragraph beginning 'Here we show' and the subsequent general-framework section).
minor comments (2)
  1. [Abstract] The abstract uses the abbreviation 'NH { crystals}' with an apparent formatting artifact; this should be rendered consistently as 'non-Hermitian crystals' or defined on first use.
  2. [Discussion of exceptional points] The claim that EFBs 'persist beyond these singularities' would benefit from an explicit statement of the parameter range or analytic continuation used to establish persistence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive criticism. We address the major comment below and have revised the manuscript to include the requested explicit derivation.

read point-by-point responses

  1. Referee: The load-bearing assumption that a momentum-independent eigenvalue on the majority sublattice remains exactly k-independent (and retains its algebraic multiplicity) after arbitrary non-Hermitian perturbations is not demonstrated for general block forms. In a general NH bipartite Hamiltonian the off-diagonal blocks carry complex momentum dependence; their product with the inverse of the minority block can feed k-dependent corrections back into the effective equation for the majority eigenvalue, shifting the root or reducing multiplicity. The manuscript must supply the explicit characteristic equation or block-diagonalization step showing that this feedback vanishes for arbitrary gain/loss and complex couplings (see the paragraph beginning 'Here we show' and the subsequent general-framework section).

    Authors: We thank the referee for this precise observation on the general framework. The bipartite NH Hamiltonian is taken with a momentum-independent block on the majority sublattice by construction (constant chemical potential), so the candidate flat-band energy λ coincides with a zero block in (H − λI). Consider the block form H(k) = [[ε I_{N1}, T(k)], [T'(k), δ I_{N2}]] with N1 > N2 and δ = ε2 − ε. Setting λ = ε yields the shifted operator [[0, T(k)], [T'(k), δ I]]. The eigenvalue equation then decouples into T(k) v2 = 0 and T'(k) v1 + δ v2 = 0. For generic complex T(k) of size N1 × N2 the rank is N2, so dim ker T(k) ≥ N1 − N2 independently of k. Each such v2 lies in the image of the underdetermined map T'(k) (N2 × N1), which is surjective for generic couplings; hence a solution v1 always exists. The resulting kernel dimension is therefore at least N1 − N2 for every k, with no k-dependent shift or loss of multiplicity. Because the majority block is identically zero, the Schur complement involving the inverse of the minority block is never formed and no feedback term appears. This argument uses only linear algebra and holds for arbitrary complex, non-reciprocal T(k) and T'(k). We have inserted the full block-diagonalization, the characteristic-equation reduction, and the kernel-dimension count into the revised general-framework section. revision: yes

Circularity Check

0 steps flagged

No circularity: generalization rests on independent counting argument

full rationale

The paper's central claim extends the Hermitian sublattice-degeneracy-mismatch principle to the non-Hermitian regime by asserting that a momentum-independent eigenvalue on one sublattice, when its degeneracy exceeds that of the partner sublattice, produces flat bands irrespective of gain/loss or complex couplings. This counting argument is presented directly in the abstract without reduction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work. No equations are shown that define the flat-band condition in terms of itself or rename a known result; the derivation remains self-contained and does not collapse to its inputs by construction. The skeptic concern addresses validity under general perturbations rather than logical circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The construction relies on the standard eigenvalue problem for a bipartite lattice and the assumption that one sublattice eigenvalue remains momentum-independent; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The eigenvalue on one sublattice is momentum-independent and its degeneracy exceeds that of the partner sublattice.
    Invoked in the sentence 'whenever one sublattice hosts a momentum-independent eigenvalue with degeneracy exceeding that of its partner'.

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Forward citations

Cited by 2 Pith papers

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Reference graph

Works this paper leans on

108 extracted references · 108 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    2rk dispersive states given by Ψ± n,k,R = 1√ 2 √ 1−α2 ( ±√1 +αϕn,k√1−αψn,k ) , with E± n,k =± √ 1−α2ϵn,k

    work page

  2. [2]

    NA−rk zero-modes given by the non-null kernel of S† k, as Ψn,k,R = (ϕn,k 0 ) , with En,k = 0

    work page

  3. [3]

    Here, weassumenormalizationofthesingulareigenstates ψ† n,kψn,k =ϕ† n,kϕn,k = 1

    NB−rk zero-modes that arise whenSk is not full- rank, i.e.rk <N B, given by Ψn,k,R = ( 0 ψn,k ) , with En,k = 0. Here, weassumenormalizationofthesingulareigenstates ψ† n,kψn,k =ϕ† n,kϕn,k = 1. This is shown in Eqs. (5) and (6) in the main text. Remarkably, the flat-band states retain the same form as in the Hermitian case [37], and the NH contribution onl...

    work page

  4. [4]

    2rk dispersive states given by Ψ± n,k,R = 1√ (δµ±∆ k)2 + (1−α2)ϵ2 n,k ( (δµ±∆ k)ϕn,k (1−α)ϵn,kψn,k ) , with E± n,k = ¯µ±∆ k. 7

    work page

  5. [5]

    NA−rk flat-band states given by Ψn,k,R = (ϕn,k 0 ) , with En,k =µA

    work page

  6. [6]

    Here the standard flat-band states that depend only on the sublattice imbalanceNA−NB̸= 0 retain exactly their Hermitian form

    NB−rk flat-band states whenSk is not full-rank given by Ψn,k,R = ( 0 ψn,k ) , with En,k =µB. Here the standard flat-band states that depend only on the sublattice imbalanceNA−NB̸= 0 retain exactly their Hermitian form. By contrast, the dispersive sec- tor acquires a non-trivialα-dependence which, together with its momentum dependence, yields a richer patt...

    work page

  7. [7]

    E. J. Bergholtz and Z. Liu, Topological flat band models and fractional chern insulators, International Journal of Modern Physics B27, 1330017 (2013)

    work page 2013

  8. [8]

    S. A. Parameswaran, R. Roy, and S. L. Sondhi, Frac- tional quantum hall physics in topological flat bands, Comptes Rendus Physique 14, 816 (2013), topological insulators / Isolants topologiques

    work page 2013

  9. [9]

    T. T. Heikkilä and G. E. Volovik, Flat bands as a route to high-temperature superconductivity in graphite, in Basic Physics of Functionalized Graphite (Springer,

    work page

  10. [10]

    G. E. Volovik, Graphite, graphene, and the flat band superconductivity, JETP Letters107, 516 (2018)

    work page 2018

  11. [11]

    Roy and V

    B. Roy and V. Juričić, Unconventional superconduc- tivity in nearly flat bands in twisted bilayer graphene, Phys. Rev. B99, 121407 (2019)

    work page 2019

  12. [12]

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, et al., Correlated insulator behaviour at half-filling in magic-angle graphene super- lattices, Nature 556, 80 (2018)

    work page 2018

  13. [13]

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T.Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional su- perconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018)

    work page 2018

  14. [14]

    Y. Cao, D. Rodan-Legrain, J. M. Park, N. F. Q. Yuan, K. Watanabe, T. Taniguchi, R. M. Fernandes, L. Fu, andP.Jarillo-Herrero,Nematicityandcompetingorders in superconducting magic-angle graphene, Science372, 264 (2021)

    work page 2021

  15. [15]

    Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Kha- laf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. For- rester, et al., Fractional chern insulators in magic-angle twisted bilayer graphene, Nature600, 439 (2021)

    work page 2021

  16. [16]

    J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Flavour hund’s coupling, chern gaps and charge diffusivity in moiré graphene, Nature592, 43 (2021). 9

    work page 2021

  17. [17]

    I. Das, X. Lu, J. Herzog-Arbeitman, Z.-D. Song, K. Watanabe, T. Taniguchi, B. A. Bernevig, and D. K. Efetov, Symmetry-broken chern insulators and rashba-like landau-level crossings in magic-angle bilayer graphene, Nature Physics17, 710 (2021)

    work page 2021

  18. [18]

    Y. Choi, H. Kim, Y. Peng, A. Thomson, C. Lewandowski, R. Polski, Y. Zhang, H. S. Arora, K. Watanabe, T. Taniguchi,et al., Correlation-driven topological phases in magic-angle twisted bilayer graphene, Nature 589, 536 (2021)

    work page 2021

  19. [19]

    Sánchez Sánchez, I

    M. Sánchez Sánchez, I. Díaz, J. González, and T. Stauber, Nematic versus kekulé phases in twisted bi- layer graphene under hydrostatic pressure, Phys. Rev. Lett. 133, 266603 (2024)

    work page 2024

  20. [20]

    Suárez Morell, J

    E. Suárez Morell, J. D. Correa, P. Vargas, M. Pacheco, and Z. Barticevic, Flat bands in slightly twisted bilayer graphene: Tight-binding calculations, Phys. Rev. B82, 121407 (2010)

    work page 2010

  21. [21]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proceedings of the Na- tional Academy of Sciences108, 12233 (2011)

    work page 2011

  22. [22]

    J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Graphene bilayer with a twist: Electronic structure, Phys. Rev. Lett.99, 256802 (2007)

    work page 2007

  23. [23]

    Kang and O

    J. Kang and O. Vafek, Symmetry, maximally localized wannier states, and a low-energy model for twisted bi- layer graphene narrow bands, Phys. Rev. X8, 031088 (2018)

    work page 2018

  24. [24]

    H. C. Po, L. Zou, T. Senthil, and A. Vishwanath, Faith- ful tight-binding models and fragile topology of magic- angle bilayer graphene, Phys. Rev. B99, 195455 (2019)

    work page 2019

  25. [25]

    M. P. Shores, E. A. Nytko, B. M. Bartlett, and D. G. Nocera, A structurally perfect s= 1/2 kagomé antiferro- magnet, Journal of the american chemical society127, 13462 (2005)

    work page 2005

  26. [26]

    Mendels and F

    P. Mendels and F. Bert, Quantum kagome antiferro- magnet zncu3(oh)6cl2, Journal of the Physical Society of Japan 79, 011001 (2010)

    work page 2010

  27. [27]

    T.-H. Han, J. S. Helton, S. Chu, D. G. Nocera, J. A. Rodriguez-Rivera, C. Broholm, and Y. S. Lee, Fraction- alized excitations in the spin-liquid state of a kagome- lattice antiferromagnet, Nature492, 406 (2012)

    work page 2012

  28. [28]

    Mazin, H

    I. Mazin, H. O. Jeschke, F. Lechermann, H. Lee, M. Fink, R. Thomale, and R. Valentí, Theoretical pre- dictionofastronglycorrelateddiracmetal,Naturecom- munications 5, 4261 (2014)

    work page 2014

  29. [29]

    S. Lisi, X. Lu, T. Benschop, T. A. de Jong, P. Stepanov, J. R. Duran, F. Margot, I. Cucchi, E. Cappelli, A. Hunter, et al., Observation of flat bands in twisted bilayer graphene, Nature Physics17, 189 (2021)

    work page 2021

  30. [30]

    I. Hase, Y. Higashi, H. Eisaki, and K. Kawashima, New three-dimensional flat band candidate materials pb2as2o7 and pb2sn2o7, Scientific Reports 14, 26532 (2024)

    work page 2024

  31. [31]

    Nakata, T

    Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, Observation of flat band for terahertz spoof plasmons in a metallic kagomé lattice, Phys. Rev. B85, 205128 (2012)

    work page 2012

  32. [32]

    Kajiwara, Y

    S. Kajiwara, Y. Urade, Y. Nakata, T. Nakanishi, and M. Kitano, Observation of a nonradiative flat band for spoof surface plasmons in a metallic lieb lattice, Phys. Rev. B 93, 075126 (2016)

    work page 2016

  33. [33]

    H. Wang, B. Yang, W. Xu, Y. Fan, Q. Guo, Z. Zhu, and C. T. Chan, Highly degenerate photonic flat bands arising from complete graph configurations, Phys. Rev. A 100, 043841 (2019)

    work page 2019

  34. [34]

    Takeda, T

    H. Takeda, T. Takashima, and K. Yoshino, Flat pho- tonic bands in two-dimensional photonic crystals with kagome lattices, Journal of Physics: Condensed Matter 16, 6317 (2004)

    work page 2004

  35. [35]

    R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, Observation of localized states in lieb pho- tonic lattices, Phys. Rev. Lett.114, 245503 (2015)

    work page 2015

  36. [36]

    Baboux, L

    F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, Bosonic condensation and disorder-induced localization in a flat band, Phys. Rev. Lett. 116, 066402 (2016)

    work page 2016

  37. [37]

    Mukherjee, A

    S. Mukherjee, A. Spracklen, D. Choudhury, N. Gold- man, P. Öhberg, E. Andersson, and R. R. Thomson, Observation of a localized flat-band state in a photonic lieb lattice, Phys. Rev. Lett.114, 245504 (2015)

    work page 2015

  38. [38]

    Y.-C. He, F. Grusdt, A. Kaufman, M. Greiner, and A. Vishwanath, Realizing and adiabatically preparing bosonic integer and fractional quantum hall states in optical lattices, Phys. Rev. B96, 201103 (2017)

    work page 2017

  39. [39]

    N. R. Cooper, J. Dalibard, and I. B. Spielman, Topo- logical bands for ultracold atoms, Rev. Mod. Phys.91, 015005 (2019)

    work page 2019

  40. [40]

    Zeng, Y.-R

    C. Zeng, Y.-R. Shi, Y.-Y. Mao, F.-F. Wu, Y.-J. Xie, T. Yuan, H.-N. Dai, and Y.-A. Chen, Observation of flat-band localized state in a one-dimensional diamond momentum lattice of ultracold atoms, Chinese Physics B 33, 010303 (2023)

    work page 2023

  41. [41]

    W. Sui, W. Han, Z. V. Han, Z. Meng, and J. Zhang, Topologically nontrivial and trivial flat bands via weak and strong interlayer coupling in twisted bilayer honey- comb optical lattices for ultracold atoms, Phys. Rev. A 111, 063306 (2025)

    work page 2025

  42. [42]

    D.-S. Ma, Y. Xu, C. S. Chiu, N. Regnault, A. A. Houck, Z. Song, and B. A. Bernevig, Spin-orbit-induced topo- logical flat bands in line and split graphs of bipartite lattices, Phys. Rev. Lett.125, 266403 (2020)

    work page 2020

  43. [43]

    Călugăru, A

    D. Călugăru, A. Chew, L. Elcoro, Y. Xu, N. Regnault, Z.-D. Song, and B. A. Bernevig, General construction and topological classification of crystalline flat bands, Nature Physics 18, 185 (2022)

    work page 2022

  44. [44]

    Hwang, J.-W

    Y. Hwang, J.-W. Rhim, and B.-J. Yang, General con- struction of flat bands with and without band crossings based on wave function singularity, Phys. Rev. B104, 085144 (2021)

    work page 2021

  45. [45]

    Kim, C.-g

    H. Kim, C.-g. Oh, and J.-W. Rhim, General construc- tion scheme for geometrically nontrivial flat band mod- els, Communications Physics6, 305 (2023)

    work page 2023

  46. [46]

    Leykam, S

    D. Leykam, S. Flach, and Y. D. Chong, Flat bands in lattices with non-hermitian coupling, Phys. Rev. B96, 064305 (2017)

    work page 2017

  47. [47]

    Ramezani, Non-hermiticity-induced flat band, Phys

    H. Ramezani, Non-hermiticity-induced flat band, Phys. Rev. A 96, 011802 (2017)

    work page 2017

  48. [48]

    A. A. Zyuzin and A. Y. Zyuzin, Flat band in disorder- driven non-hermitian weyl semimetals, Phys. Rev. B97, 041203 (2018)

    work page 2018

  49. [49]

    S. M. Zhang and L. Jin, Flat band in two-dimensional non-hermitian optical lattices, Phys. Rev. A 100, 043808 (2019)

    work page 2019

  50. [50]

    Jin, Flat band induced by the interplay of synthetic magnetic flux and non-hermiticity, Phys

    L. Jin, Flat band induced by the interplay of synthetic magnetic flux and non-hermiticity, Phys. Rev. A 99, 10 033810 (2019)

    work page 2019

  51. [51]

    Maimaiti and A

    W. Maimaiti and A. Andreanov, Non-hermitian flat- band generator in one dimension, Phys. Rev. B 104, 035115 (2021)

    work page 2021

  52. [52]

    L. Ding, Z. Lin, S. Ke, B. Wang, and P. Lu, Non- hermitian flat bands in rhombic microring resonator ar- rays, Opt. Express29, 24373 (2021)

    work page 2021

  53. [53]

    Talkington and M

    S. Talkington and M. Claassen, Dissipation-induced flat bands, Phys. Rev. B106, L161109 (2022)

    work page 2022

  54. [54]

    Jiang, W

    X.-P. Jiang, W. Zeng, Y. Hu, and P. Liu, Exact non- hermitian mobility edges and robust flat bands in two- dimensional lieb lattices with imaginary quasiperiodic potentials, New Journal of Physics26, 083020 (2024)

    work page 2024

  55. [55]

    Amelio and N

    I. Amelio and N. Goldman, Lasing in non-hermitian flat bands: Quantum geometry, coherence, and the fate of kardar-parisi-zhang physics, Phys. Rev. Lett. 132, 186902 (2024)

    work page 2024

  56. [56]

    Banerjee, A

    A. Banerjee, A. Bandyopadhyay, R. Sarkar, and A. Narayan, Non-hermitian topology and flat bands via an exact real-space decimation scheme, Phys. Rev. B 110, 085431 (2024)

    work page 2024

  57. [57]

    C. A. Leong and B. Roy, Non-hermitian catalysis of density-wave orders on euclidean and hyperbolic lattices (2025), arXiv:2501.18591 [cond-mat.str-el]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  58. [58]

    Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Hi- gashikawa, and M. Ueda, Topological Phases of Non- Hermitian Systems, Phys. Rev. X8, 031079 (2018)

    work page 2018

  59. [59]

    L. E. F. Foa Torres, Perspective on topological states of non-hermitian lattices, Journal of Physics: Materials3, 014002 (2019)

    work page 2019

  60. [60]

    E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Excep- tional topology of non-hermitian systems, Rev. Mod. Phys. 93, 015005 (2021)

    work page 2021

  61. [61]

    W. D. Heiss, The physics of exceptional points, Journal of Physics A: Mathematical and Theoretical45, 444016 (2012)

    work page 2012

  62. [62]

    W. Hu, H. Wang, P. P. Shum, and Y. D. Chong, Ex- ceptional points in a non-hermitian topological pump, Phys. Rev. B95, 184306 (2017)

    work page 2017

  63. [63]

    V. M. Martinez Alvarez, J. E. Barrios Vargas, and L. E. F. Foa Torres, Non-hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points, Phys. Rev. B 97, 121401 (2018)

    work page 2018

  64. [64]

    Kawabata, T

    K. Kawabata, T. Bessho, and M. Sato, Classification of exceptional points and non-hermitian topological semimetals, Phys. Rev. Lett.123, 066405 (2019)

    work page 2019

  65. [65]

    Kozii and L

    V. Kozii and L. Fu, Non-Hermitian topological theory of finite-lifetime quasiparticles: Prediction of bulk Fermi arc due to exceptional point, Phys. Rev. B109, 235139 (2024)

    work page 2024

  66. [66]

    Juričić and B

    V. Juričić and B. Roy, Yukawa-Lorentz symmetry in non-Hermitian Dirac materials, Communications Physics 7, 169 (2024)

    work page 2024

  67. [67]

    X.-J. Yu, Z. Pan, L. Xu, and Z.-X. Li, Non-hermitian strongly interacting dirac fermions, Phys. Rev. Lett. 132, 116503 (2024)

    work page 2024

  68. [68]

    S. A. Murshed and B. Roy, Quantum electrodynamics of non-Hermitian Dirac fermions, Journal of High Energy Physics 2024, 1 (2024)

    work page 2024

  69. [69]

    S. A. Murshed and B. Roy, Yukawa-Lorentz sym- metry of interacting non-Hermitian birefringent Dirac fermions, SciPost Phys.18, 073 (2025)

    work page 2025

  70. [70]

    Pino-Alarcón and V

    S. Pino-Alarcón and V. Juričić, Yukawa-lorentz symme- try of tilted non-hermitian dirac semimetals at quantum criticality, Phys. Rev. B111, 195126 (2025)

    work page 2025

  71. [71]

    J. P. Esparza and V. Juričić, Exceptional magic angles in non-hermitian twisted bilayer graphene, Phys. Rev. Lett. 134, 226602 (2025)

    work page 2025

  72. [72]

    Huang, Exceptional topology in non-hermitian twisted bilayer graphene, Phys

    Y. Huang, Exceptional topology in non-hermitian twisted bilayer graphene, Phys. Rev. B 111, 085120 (2025)

    work page 2025

  73. [73]

    Jin, Topological phases and edge states in a non- hermitian trimerized optical lattice, Phys

    L. Jin, Topological phases and edge states in a non- hermitian trimerized optical lattice, Phys. Rev. A96, 032103 (2017)

    work page 2017

  74. [74]

    X. Zhou, S. K. Gupta, Z. Huang, Z. Yan, P. Zhan, Z. Chen, M. Lu, and Z. Wang, Optical lat- tices with higher-order exceptional points by non- hermitian coupling, Applied Physics Letters 113, https://doi.org/10.1063/1.5043279 (2018)

    work page doi:10.1063/1.5043279 2018

  75. [75]

    M. Pan, H. Zhao, P. Miao, S. Longhi, and L. Feng, Photonic zero mode in a non-hermitian photonic lattice, Nature communications 9, 1308 (2018)

    work page 2018

  76. [76]

    W. Song, W. Sun, C. Chen, Q. Song, S. Xiao, S. Zhu, and T. Li, Breakup and recovery of topological zero modes in finite non-hermitian optical lattices, Phys. Rev. Lett. 123, 165701 (2019)

    work page 2019

  77. [77]

    Zhang, X

    Y. Zhang, X. Dai, and Y. Xiang, Topological hierarchy in non-hermitian three-dimensional photonic crystals, Phys. Rev. B110, 104103 (2024)

    work page 2024

  78. [78]

    L. Li, C. H. Lee, and J. Gong, Topological switch for non-hermitian skin effect in cold-atom systems with loss, Phys. Rev. Lett.124, 250402 (2020)

    work page 2020

  79. [79]

    L. Zhou, H. Li, W. Yi, and X. Cui, Engineering non- hermitian skin effect with band topology in ultracold gases, Communications Physics5, 252 (2022)

    work page 2022

  80. [80]

    Liang, D

    Q. Liang, D. Xie, Z. Dong, H. Li, H. Li, B. Gad- way, W. Yi, and B. Yan, Dynamic signatures of non- hermitian skin effect and topology in ultracold atoms, Phys. Rev. Lett.129, 070401 (2022)

    work page 2022

Showing first 80 references.