First principles calculation of topological invariants of non-Hermitian photonic crystals

Prudêncio, Filipa R.; Silveirinha, Mário G.

doi:10.1038/s42005-020-00482-3

Cited by 15 publications

(8 citation statements)

References 64 publications

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“…Chern number is used as the topological invariant of non-Hermitian systems with broken time symmetry [29]. For topological systems with spin degree of freedom, the Wilson loop classifies their different topological properties [30].…”

Section: Wilson Loop Characterizationmentioning

confidence: 99%

Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals

Chen,

Jiang,

Zhang

et al. 2021

Preprint

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The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with C6v symmetry and the PC-air-PC interface are studied based on first-principle calculation. To illustrate the importance of parity-time (PT) symmetry, three systems are considered, namely the PT-symmetric, PT-asymmetric, and lossy systems. We find that the system with gain and loss distributed in a PT symmetric manner exhibits a phase transition from a PT exact phase to a PT broken phase as the strength of the gain and loss increases, while for the PT-asymmetric and lossy systems, no such phase transition occurs. Furthermore, based on the Wilson loop calculation, the topology of the PT-symmetric system in the PT exact phase is demonstrated to keep unchanged as the Hermitian system. At last, different kinds of edge states in Hermitian systems under the influences of gain and loss are studied and we find that while the eigenfrequencies of nontrivial edge states become complex conjugate pairs, they keep real for the trivial defect states.

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Section: Wilson Loop Characterizationmentioning

confidence: 99%

Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals

Chen,

Jiang,

Zhang

et al. 2021

Preprint

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“…In a recent series of works [19,23,24], we introduced a general Green's function formalism to calculate the gap Chern numbers of non-Hermitian and possibly dispersive photonic crystals. In its most general form, the spectrum of the system under study is determined by a generic differential operator Lk (which is not required to be Hermitian) and by a multiplication (matrix) operator M g , which determine a generalized eigenvalue problem Lk…”

Section: Topological Classification With Green's Functionmentioning

confidence: 99%

“…In Reference [22], the topological phases of the photonic system were determined relying on a tight-binding approximation. Here, building on these previous works, we use an exact Green's function method [19,[23][24][25] to calculate from "first principles" the topological invariants of the Haldane photonic crystal.…”

Section: Introductionmentioning

confidence: 99%

First Principles Calculation of the Topological Phases of the Photonic Haldane Model

Prudêncio

Silveirinha

2021

Symmetry

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Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed-matter systems, as it unveiled that a broken time-reversal symmetry is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo-Tellegen coupling. Here, we use Green’s function method to determine from “first principles” the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo-Tellegen parameter.

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“…Also related to our work here, complex band structures in non-Hermitian photonic crystals have been well studied, particularly in work focusing on PT -symmetry, exceptional points and unidirectional transmission [38][39][40]. There have also been various studies on non-Hermitian topological band structure in photonic crystals [41,42] but these studies focus only on line-gap topology. To the best of our knowledge, no previous studies have investigated non-Hermitian topological photonic crystals from a point-gap topology perspective.…”

Section: Introductionmentioning

confidence: 96%

Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals

Zhong,

Wang,

Park

et al. 2021

Preprint

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We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit non-trivial point gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be either made of lossy isotropic media which is reciprocal, or lossy magneto-optical media which is non-reciprocal. We discuss the effects of reciprocity on the properties of the point gap topology. We also show that such a non-trivial point gap topology leads to non-Hermitian skin effect when the photonic crystal is truncated. In contrast to most previous studies on point gap topology which used tight-binding models, our work indicates that such non-Hermitian topology can studied in photonic crystals, which represent a more realistic system that has technological significance.

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First principles calculation of topological invariants of non-Hermitian photonic crystals

Cited by 15 publications

References 64 publications

Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals

Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals

First Principles Calculation of the Topological Phases of the Photonic Haldane Model

Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals

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