Photonic Topological Insulating Phase Induced Solely by Gain and Loss

Takata, Kenta; Notomi, Masaya

doi:10.1103/physrevlett.121.213902

Cited by 252 publications

(126 citation statements)

References 97 publications

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“…Finally, we note that, while the AAH and Nelson-Hatano Hamiltonians are related one another by a similarity transformation, the non-Hermitian skin effect observed in the latter model, i.e. the shrinking of all bulk states into one edge of the lattice [35], is not found in the AAH model.…”

mentioning

confidence: 81%

Topological Phase Transition in non-Hermitian Quasicrystals

2019

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The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian models, such as failure of the conventional bulk-boundary correspondence and non-Hermitian skin effect. Advances in the understanding of the topological properties of non-Hermitian lattices with translational invariance have been reported in several recent studies, however little is known about non-Hermitian quasicrystals. Here we disclose topological phases in a quasicrystal with parity-time (PT ) symmetry, described by a non-Hermitian extension of the Aubry-André-Harper model. It is shown that the metal-insulating phase transition, observed at the PT symmetry breaking point, is of topological nature and can be expressed in terms of a winding number. A photonic realization of a non-Hermitian quasicrystal is also suggested.Introduction. The discovery of topological phases of matter has introduced a major twist in condensed matter physics [1, 2] with great impact in other areas of physics, such as photonics, atom optics, acoustics and mechanics [3][4][5][6][7][8]. Topological band theory classifies Hermitian topological systems depending on their dimensionality and symmetries [9, 10]. The bulk topological invariants are uniquely reflected in robust edge states localized at open boundaries. The ability to engineer non-Hermitian Hamiltonians, demonstrated in a series of recent experiments [11][12][13][14][15][16][17], and the related observation of unconventional topological boundary modes sparked a great interest to extend topological band theory to open systems . Striking features are the failure of the conventional bulk-boundary correspondence [27,31,35,[37][38][39], eigenstate condensation [30,31], non-Hermitian skin effect [33,37,38], and the sensitivity of the bulk spectra on boundary conditions [19,36,[39][40][41]. Most of previous studies have concerned with crystals, however little is know about topological properties of non-Hermitian quasicrystals. Quasicrystals (QCs) constitute an intermediate phase between fully periodic lattices and fully disordered media, showing a longrange order but no periodicity [42,43]. A paradigmatic model of a one-dimensional (1D) QC is provided by the Aubry-André-Harper (AAH) Hamiltonian [43][44][45], which is known to show a metal-insulator phase transition [44][45][46]. In the Hermitian case, the AAH Hamiltonian is topologically nontrivial because it can be mapped into a two-dimensional quantum Hall system on a square lattice [47][48][49][50]. A few recent studies have considered some non-Hermitian extensions of the AAH model [51][52][53][54][55][56], mainly with a commensurate potential and with open boundary conditions. Such numerical studies investigated how gain and loss distributions affect edge states and parity-time (PT ) symmetry breaking [51][52][53]55], the Hofstadter butterfly spectrum [52], and the localization properties of eig...

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confidence: 81%

Topological Phase Transition in non-Hermitian Quasicrystals

2019

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“…For the SSH model with PT -symmetry in our cases, it possesses pseudo-anti-Hermiticity ΓĤ (β) † = −Ĥ (β) Γ with β = {b, c} which leads to nontrivial topology for non-Hermitian cases [39,40,82,83] and arouses the eigenvalues with the form ±ã ± ib whereã andb depend on J − , J + and γ [55]. In the following, we consider the spectra and size-dependent edge modes of SSH model subjected to different gain and loss on-site potentials shown in Fig.1…”

Section: Ssh Model With Pt -Symmetrymentioning

confidence: 95%

Fate of zero modes in a finite Su-Schrieffer-Heeger model with PT symmetry

Zhang

Chen

et al. 2020

Phys. Rev. A

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Due to the boundary coupling in a finite system, the zero modes of a standard Su-Schrieffer-Heeger (SSH) model may deviate from exact-zero energy. A recent experiment has shown that by increasing the system size or the altering gain or loss strength of the SSH model with parity-time (PT ) symmetry, the real parts of the energies of the edge modes can be recovered to exact-zero value [W. Song et al. Phys. Rev. Lett. 123, 165701 (2019)]. To clarify the effects of PT -symmetric potentials on the recovery of the nontrivial zero modes, we study the SSH model with different forms of PT -symmetric potentials in both infinite and finite systems. Our results indicate that the energies of the edge modes in infinite size cases decide whether or not the success of the recovery of the zero modes by tuning the strength of PT -symmetric potential in a finite system. If the energies of the edge modes amount to zero in the thermodynamic limit under open boundary condition (OBC), the recovery of the zero modes will break down by increasing the gain or loss strength for a finite system. Our results can be easily examined in different experimental platforms and inspire more insightful understanding on nontrivial edge modes in topologically non-Hermitian systems.

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“…On contrary to Hermitian systems, topological phase transition point can not be determined by the translationally invariant form of the non-Hermitian Hamiltonian. We stress that topological phase transition can also be induced solely by gain and loss [34]. Recently, the idea of pseudo topological insulators has been introduced to explain topological edge states for massive SSH Hamiltonian [35].…”

Section: Introductionmentioning

confidence: 94%

Topological states in a non-Hermitian two-dimensional Su-Schrieffer-Heeger model

Yüce

Ramezani

2019

Phys. Rev. A

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A non-Hermitian topological insulator with real spectrum is interesting in the theory of non-Hermitian extension of topological systems. We find an experimentally realizable example of a two dimensional non-Hermitian topological insulator with real spectrum. We consider two-dimensional Su-Schrieffer-Heeger (SSH) model with gain and loss. We introduce non-Hermitian polarization vector to explore topological phase and show that topological edge states in the band gap exist in the system. PACS numbers:

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Photonic Topological Insulating Phase Induced Solely by Gain and Loss

Cited by 252 publications

References 97 publications

Topological Phase Transition in non-Hermitian Quasicrystals

Topological Phase Transition in non-Hermitian Quasicrystals

Fate of zero modes in a finite Su-Schrieffer-Heeger model with PT symmetry

Topological states in a non-Hermitian two-dimensional Su-Schrieffer-Heeger model

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