Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling

Wang, P.; Jin, Lin; Song, Z.

doi:10.1103/physreva.99.062112

Cited by 32 publications

(20 citation statements)

References 148 publications

(93 reference statements)

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“…It is also known that non-Hermiticity can explicitly disrupt the conventional bulk-boundary correspondence (BBC) held in Hermitian systems [119,130,[139][140][141][131][132][133][134][135][136][137][138]. Especially, asymmetric couplings make not only topological edge states but also non-topological bulk states localize around an either end to which the stronger hopping is directed (non-Hermitian skin effect) [ Fig.…”

Section: Complex Bandgap and Emergent Non-hermitian Topological Effectsmentioning

confidence: 99%

Active topological photonics

et al. 2020

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Topological photonics has emerged as a novel route to engineer the flow of light. Topologically-protected photonic edge modes, which are supported at the perimeters of topologically-nontrivial insulating bulk structures, have been of particular interest as they may enable low-loss optical waveguides immune to structural disorder. Very recently, there is a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolutionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of remarkable realizations are topological lasers with unidirectional light output under time-reversal symmetry breaking and topologically-protected polariton and micro/nano-cavity lasers. Moreover, the introduction of gain and loss provides a fascinating playground to explore novel topological phases, which are in close relevance to non-Hermitian and paritytime symmetric quantum physics and are in general difficult to access using fermionic condensed matter systems. Here, we review the cutting-edge research on active topological photonics, in which optical gain plays a pivotal role. We discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topological edge modes. In such demonstrations, the optical modes of the topological lasers are determined by the dielectric structures and support lasing oscillation with the help of optical gain. We also address recent researches on topological photonic systems in which gain and loss themselves essentially influence on topological properties of the bulk systems. We believe that active topological photonics provides powerful means to advance micro/nanophotonics systems for diverse applications and topological physics itself as well.

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Section: Complex Bandgap and Emergent Non-hermitian Topological Effectsmentioning

confidence: 99%

Active topological photonics

et al. 2020

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“…Resorting to the MIPR, which is used to determine the localization degree of the multi eigenstates, we now characterize the localization effect of the eigenstates caused by the asymmetric coupling and show the influence factors of the eigenstates localization quantitatively. [ 59 ] Generally, the MIPR for right eigenvector

false| ψ_{j}^{n} false⟩

is defined as [ 55,60,61 ]

MIPR = \frac{1}{L} \sum_{n = 1}^{L} \frac{\sum_{j} {false| ψ_{j}^{n} false|}^{4}}{(\sum_{j} | ψ_{j}^{n} {|^{2} false)}^{2}}

where the sum j is over the sites of lattice. When the MIPR tends to a finite stable value, the localization effect of the eigenstates is obvious and the system is in the localized state.…”

Section: Non‐hermitian Skin Effect and Mean Inverse Participation Ratiomentioning

confidence: 99%

“…[ 44–54 ] Based on the symmetric coupling threaded by an imaginary gauge field, the non‐Hermitian phase transition and eigenstate localization in a normal non‐Hermitian system has been illustrated in ref. [55]. But in the non‐Hermitian Su–Schrieffer–Heeger (SSH) model, it is not yet clearly revealed.…”

Section: Introductionmentioning

confidence: 99%

Topological Phase Transition and Eigenstates Localization in a Generalized Non‐Hermitian Su–Schrieffer–Heeger Model

Zhang

Huang

et al. 2020

Annalen der Physik

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The topological properties of a generalized non‐Hermitian Su–Schrieffer–Heeger model are investigated and it is demonstrated that the non‐Hermitian phase transition and the non‐Hermitian skin effect can be induced by intra‐cell asymmetric coupling under open boundary conditions. Through investigating and calculating the non‐Hermitian winding number with generalized Brillouin zone theory, it is found that the present non‐Hermitian system has an exact bulk‐boundary correspondence relationship. Meanwhile, the non‐Hermitian winding number is used to characterize the non‐Hermitian phase transition and determine the phase transition boundary, and it is found that the non‐Hermitian phase transition is not completely induced by the asymmetric coupling strength. By means of the mean inverse participation ratio, the factors that affect the eigenstates localization are shown and it is revealed that large system size or large asymmetric coupling strength can leave the system in the localized state. Additionally, it is found that for the asymmetric coupling strength and the system size, the eigenstates localization is much more sensitive to the asymmetric coupling strength.

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“…Notably, the bulk-boundary correspondence fails in some non-Hermitian topological systems [57,61,99,[129][130][131][132][133][134][135][136][137][138][139][140][141][142]. The spectrum under the periodical boundary condition (PBC) significantly differs from that under the open boundary condition (OBC), and the eigenstates under OBC are all localized at the system boundary (the non-Hermitian skin effect) [133].…”

Section: Introductionmentioning

confidence: 99%

“…The topological invariant can be constructed either from the biorthogonal norm [57], the non-Bloch bulk [61,133], or the singular-value decomposition of the Hamiltonian [140]. The reason for the breakdown of bulk-boundary correspondence is that an asymmetric coupling induces an imaginary Aharonov-Bohm effect [134,135]; the validity of the bulk-boundary correspondence can be maintained by chiral-inversion symmetry [134]. The boundary modes in non-Hermitian systems have been discussed on the basis of the transfer matrix method [143] and the Green's function method [85,144,145].…”

Section: Introductionmentioning

confidence: 99%

Inversion symmetric non-Hermitian Chern insulator

Jin

Song

2019

Phys. Rev. B

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We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial phase. The band touching points are isolated and protected by the symmetry. The band touching affects the existence of helical edge states. Moreover, topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction. The detaching points between the edge states and the bulk states are predicted by the winding number associated with the vector field of average values of Pauli matrices. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.

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Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling

Cited by 32 publications

References 148 publications

Active topological photonics

Active topological photonics

Topological Phase Transition and Eigenstates Localization in a Generalized Non‐Hermitian Su–Schrieffer–Heeger Model

Inversion symmetric non-Hermitian Chern insulator

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