Finite-size effects in non-Hermitian topological systems

Chen, Rui; Chen, Chui-Zhen; Zhou, Bin; Xu, Dong-Hui

doi:10.1103/physrevb.99.155431

Cited by 54 publications

(32 citation statements)

References 102 publications

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“…Our main findings in the present paper are unique to an open chain showing the non-Hermitian skin effect due to the complex Bloch wave number. Therefore they cannot be studied through the previous works [102][103][104][105][106][107][108] on the energy spectrum, the eigenstates, and the topological invariant in the non-Hermitian SSH model with periodic boundary conditions.…”

Section: Appendix B: Previous Work On the Non-hermitian Ssh Modelmentioning

confidence: 99%

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Yokomizo

Murakami

2020

Phys. Rev. Research

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Energy bands of non-Hermitian crystalline systems are described in terms of the generalized Brillouin zone (GBZ) having unique features which are absent in Hermitian systems. In this paper, we show that in one-dimensional non-Hermitian systems with both sublattice symmetry and time-reversal symmetry such as the non-Hermitian Su-Schrieffer-Heeger model, a topological semimetal phase with exceptional points is stabilized by the unique features of the GBZ. Namely, under a change of a system parameter, the GBZ is deformed so that the system remains gapless. It is also shown that each energy band is divided into three regions, depending on the symmetry of the eigenstates, and the regions are separated by the cusps and the exceptional points in the GBZ.

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Section: Appendix B: Previous Work On the Non-hermitian Ssh Modelmentioning

confidence: 99%

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Yokomizo

Murakami

2020

Phys. Rev. Research

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“…Even so, the existence of topologically protected edge modes is often desired. The question of the existence of BEC is a topic currently of great interest in the field of non-Hermitian TIs [34][35][36][37][38][39][40][41][42][43], where some propose new topological numbers specific to non-Hermiticity [44]. Hermitian systems can also exhibit BEC breakdown due to breaking of the symmetry that protects the edge modes [45].…”

Section: Introductionmentioning

confidence: 99%

Bulk-edge correspondence and long-range hopping in the topological plasmonic chain

2019

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The existence of topologically protected edge modes is often cited as a highly desirable trait of topological insulators. However, these edge states are not always present. A realistic physical treatment of long range hopping in a one-dimensional dipolar system can break the symmetry that protects the edge modes without affecting the bulk topological number, leading to a breakdown in bulk-edge correspondence. It is important to find a better understanding of where and how this occurs, as well as how to measure it. Here we examine the behaviour of the bulk and edge modes in a dimerised chain of metallic nanoparticles and in a simpler non-Hermitian next-nearest-neighbour model to provide some insight into the phenomena of bulk-edge breakdown. We construct bulk-edge correspondence phase diagrams for the simpler case and use these ideas to devise a measure of symmetry-breaking for the plasmonic system based on its bulk properties. This provides a parameter regime for which bulk-edge correspondence is preserved in the topological plasmonic chain, as well as a framework for assessing this phenomenon in other systems. arXiv:1902.00467v2 [cond-mat.mes-hall]

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“…It is important to realize that the advantageous properties of topological wave systems, especially in acoustics, are often mitigated by the presence of dissipation losses, imposing certain restrictions on the available bandwidth of operation or propagation length of the topological edge modes. Studying the effect of losses on the topological phases of matter is therefore an emerging direction of research, which has recently inspired the new field of non-Hermitian topological insulators [437][438][439][440][441][442][443][444][445][446][447][448][449][450][451][452][453]. By exploiting the interplay between gain, loss and coupling strengths, such types of insulating phases allow one to go beyond the restrictions of Hermitian topological insulators, especially their sensitivity to absorption losses.…”

Section: Discussionmentioning

confidence: 99%

Topological wave insulators: a review

Zangeneh-Nejad¹,

Alù²,

Fleury³

2020

Comptes Rendus. Physique

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Originally discovered in condensed matter systems, topological insulators (TIs) have been ubiquitously extended to various fields of classical wave physics including photonics, phononics, acoustics, mechanics, and microwaves. In the bulk, like any other insulator, electronic TIs exhibit an excessively high resistance to the flow of mobile charges, prohibiting metallic conduction. On their surface, however, they support one-way conductive states with inherent protection against certain types of disorder and defects, defying the common physical wisdom of electronic transport in presence of impurities. When transposed to classical waves, TIs open a wealth of exciting engineering-oriented applications, such as robust routing, lasing, signal processing, switching, etc., with unprecedented robustness against various classes of defects. In this article, we first review the basic concept of topological order applied to classical waves, starting from the simple onedimensional example of the Su-Schrieffer-Heeger (SSH) model. We then move on to two-dimensional wave TIs, discussing classical wave analogues of Chern, quantum Hall, spin-Hall, Valley-Hall, and Floquet TIs. Finally, we review the most recent developments in the field, including Weyl and nodal semimetals, higherorder topological insulators, and self-induced non-linear topological states.

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Finite-size effects in non-Hermitian topological systems

Cited by 54 publications

References 102 publications

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Bulk-edge correspondence and long-range hopping in the topological plasmonic chain

Topological wave insulators: a review

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