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Teo HT, Mandal S, Long Y, Xue H, Zhang B. Pseudomagnetic suppression of non-Hermitian skin effect. Sci Bull (Beijing) 2024; 69:1667-1673. [PMID: 38702278 DOI: 10.1016/j.scib.2024.04.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 01/23/2024] [Accepted: 04/07/2024] [Indexed: 05/06/2024]
Abstract
It has recently been shown that the non-Hermitian skin effect can be suppressed by magnetic fields. In this work, using a two-dimensional tight-binding lattice, we demonstrate that a pseudomagnetic field can also lead to the suppression of the non-Hermitian skin effect. With an increasing pseudomagnetic field, the skin modes are found to be pushed into the bulk, accompanied by the reduction of skin topological area and the restoration of Landau level energies. Our results provide a time-reversal invariant route to localization control and could be useful in various classical wave devices that are able to host the non-Hermitian skin effect but inert to magnetic fields.
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Affiliation(s)
- Hau Tian Teo
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Subhaskar Mandal
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yang Long
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Haoran Xue
- Department of Physics, The Chinese University of Hong Kong, Hong Kong 999077, China.
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore; Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore.
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Zhou L, Zhang DJ. Non-Hermitian Floquet Topological Matter-A Review. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1401. [PMID: 37895522 PMCID: PMC10606436 DOI: 10.3390/e25101401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Revised: 09/19/2023] [Accepted: 09/27/2023] [Indexed: 10/29/2023]
Abstract
The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.
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Affiliation(s)
- Longwen Zhou
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao 266100, China
- Key Laboratory of Optics and Optoelectronics, Qingdao 266100, China
- Engineering Research Center of Advanced Marine Physical Instruments and Equipment of MOE, Qingdao 266100, China
| | - Da-Jian Zhang
- Department of Physics, Shandong University, Jinan 250100, China
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Wang Q, Qian J, Jiang L. Non-Hermitian kagome photonic crystal with a totally topological spatial mode selection. OPTICS EXPRESS 2023; 31:5363-5377. [PMID: 36823818 DOI: 10.1364/oe.482836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
Recently, the study of non-Hermitian topological edge and corner states in sonic crystals (SCs) and photonic crystals (PCs) has drawn much attention. In this paper, we propose a Wannier-type higher-order topological insulator (HOTI) model based on the kagome PC containing dimer units and study its non-Hermitian topological corner states. When balanced gain and loss are introduced into the dimer units with a proper parity-time symmetric setting, the system will show asymmetric Wannier bands and can support two Hermitian corner states and two pairs of complex-conjugate or pseudo complex-conjugate non-Hermitian corner states. These topological corner states are solely confined at three corners of the triangular supercell constructed by the trivial and non-trivial kagome PCs, corresponding to a topological spatial mode selection effect. As compared to the non-Hermitian quadrupole-type HOTIs, the non-Hermitian Wannier-type HOTIs can realize totally topological spatial mode selection by using much lower coefficients of gain and loss. Our results pave the way for the development of novel non-Hermitian photonic topological devices based on Wannier-type HOTIs.
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Cheng Z, Bomantara RW, Xue H, Zhu W, Gong J, Zhang B. Observation of π/2 Modes in an Acoustic Floquet System. PHYSICAL REVIEW LETTERS 2022; 129:254301. [PMID: 36608239 DOI: 10.1103/physrevlett.129.254301] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 11/08/2022] [Indexed: 06/17/2023]
Abstract
Topological phases of matter have remained an active area of research in the last few decades. Periodic driving is a powerful tool for enriching such exotic phases, leading to various phenomena with no static analogs. One such phenomenon is the emergence of the elusive π/2 modes, i.e., a type of topological boundary state pinned at a quarter of the driving frequency. The latter may lead to the formation of Floquet parafermions in the presence of interaction, which is known to support more computational power than Majorana particles. In this Letter, we experimentally verify the signature of π/2 modes in an acoustic waveguide array, which is designed to simulate a square-root periodically driven Su-Schrieffer-Heeger model. This is accomplished by confirming the 4T-periodicity (T being the driving period) profile of an initial-boundary excitation, which we also show theoretically to be the smoking gun evidence of π/2 modes. Our findings are expected to motivate further studies of π/2 modes in quantum systems for potential technological applications.
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Affiliation(s)
- Zheyu Cheng
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Raditya Weda Bomantara
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
- Department of Physics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia
| | - Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Weiwei Zhu
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
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Liu J, Shen J, Zhao D, Zhang P. Photonic passbands induced by optical fractal effect in Cantor dielectric multilayers. PLoS One 2022; 17:e0268908. [PMID: 35917299 PMCID: PMC9345341 DOI: 10.1371/journal.pone.0268908] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 05/11/2022] [Indexed: 11/18/2022] Open
Abstract
We investigate the splitting and incorporation of optical fractal states in one-dimensional photonic quasi-crystals. The aperiodic crystals which are composed of two different dielectrics submit to Cantor sequence. Defects in Cantor crystals can greatly enhance the localization of electric field, which induces the optical fractal effect. The number of optical fractal states increases exponentially with the generation number of Cantor sequence. Moreover, the optical fractal characteristics depend on the incident angle of light, of which the fractal states may split/incorporate by modulating the value of incident angle. This study could be utilized for band-pass filters and reflectors.
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Affiliation(s)
- Jianxia Liu
- School of Electrical and Information Engineering, Hubei University of Science and Technology, Xianning, China
| | - Jing Shen
- School of Electrical and Information Engineering, Hubei University of Science and Technology, Xianning, China
| | - Dong Zhao
- School of Electrical and Information Engineering, Hubei University of Science and Technology, Xianning, China
| | - Pu Zhang
- Research Center for the Development of Rural Education and Culture, Key Research Base of Humanities and Social Sciences in Hubei Province, Hubei University of Science and Technology, Xianning, China
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Abstract
In this paper, we investigate the nonreciprocity of reflection in parity-time−symmetric (PT-symmetric) Cantor photonic crystals (PCs). Two one-dimensional PCs abiding by the Cantor sequence are PT-symmetric about the center. The PT symmetry and defect cavities in Cantor PCs can induce optical fractal states which are transmission modes. Subsequently, the left and right reflectionless states are located on both sides of a transmission peak. The invisible effect depends on the incident direction and the invisible wavelength can be modulated by the gain–loss factor. This study has potential applications in tunable optical reflectors and invisible cloaks.
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Longhi S. Bulk-edge correspondence and trapping at a non-Hermitian topological interface. OPTICS LETTERS 2021; 46:6107-6110. [PMID: 34913931 DOI: 10.1364/ol.445437] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 11/17/2021] [Indexed: 06/14/2023]
Abstract
In Hermitian systems, according to the bulk-edge correspondence, interfacing two topological optical media with different bulk topological numbers implies the existence of edge states, which can trap light at the interface. However, such a general scenario can be violated when dealing with non-Hermitian systems. Here we show that interfacing two semi-infinite Hatano-Nelson chains with different bulk topological numbers can result in the existence of infinitely many edge (interface) states; however, light waves cannot be rather generally trapped at the interface.
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Longhi S. Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation. OPTICS LETTERS 2021; 46:4470-4473. [PMID: 34525024 DOI: 10.1364/ol.440052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Accepted: 08/20/2021] [Indexed: 06/13/2023]
Abstract
Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap, the phase transition is of universal form and described by a non-Hermitian Dirac equation with Lorentz-symmetry violation. A simple photonic system displaying such a phase transition is discussed, which is based on light coupling in co-propagating gratings.
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Wu H, Wei G, Liu Z, Xiao JJ. Square-root topological state of coupled plasmonic nanoparticles in a decorated Su-Schrieffer-Heeger lattice. OPTICS LETTERS 2021; 46:4256-4259. [PMID: 34469988 DOI: 10.1364/ol.434306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
The square-root operation can generate systems with new (to the best of our knowledge) topological phases whose topological properties are inherited from the parent Hamiltonian. In this Letter, we introduce the concept of square-root topology in the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model and construct a square-root topological square nanoparticle lattice (SRTL) by inserting additional sites into the original 2D SSH model. We find that the topological states in the SRTL are intriguingly different from those in the corresponding SSH model (with on-site potential) due to the change in symmetrical characteristics. Plasmonic nanoparticle arrays are used to demonstrate this by including both nearest-neighbor and next-nearest-neighbor interactions within the dipole approximation. These unique topological states, such as the single corner mode and multiple topological edge modes, enrich the topological features produced by square-root operation and expand the scope to apply such topological features into photonic systems.
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Lin Z, Ding L, Ke S, Li X. Steering non-Hermitian skin modes by synthetic gauge fields in optical ring resonators. OPTICS LETTERS 2021; 46:3512-3515. [PMID: 34329212 DOI: 10.1364/ol.431904] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Accepted: 06/22/2021] [Indexed: 06/13/2023]
Abstract
We show that the synthetic gauge fields for photons provide a versatile approach to generate and control the non-Hermitian skin effect. By utilizing indirectly coupled optical ring resonator arrays with long-range couplings and on-site gain and loss, we find that the skin effect appears once the gauge field is not an integer multiple of π. In addition to tunable localization direction, the skin modes display anisotropic behaviors with frequency-dependent decay length, which can be explained by the split subregion of the generalized Brillouin zone (GBZ) and an effective model under adiabatic elimination. Through numerical simulation, we can also demonstrate exotic features in propagation effects enabled by the skin effect, including asymmetric transmission and reconfigurable accumulation interface. Our study paves the way to dynamically steer skin modes, which may find applications in laser, optical switch, and signal processing.
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Ding L, Lin Z, Ke S, Wang B, Lu P. Non-Hermitian flat bands in rhombic microring resonator arrays. OPTICS EXPRESS 2021; 29:24373-24386. [PMID: 34614684 DOI: 10.1364/oe.431038] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 07/05/2021] [Indexed: 06/13/2023]
Abstract
We investigate the flat bands in a quasi-one-dimensional rhombic array composed of evanescently coupled microring resonators (MRRs) with non-Hermitian coupling. By changing the relative position of non-Hermitian coupling in each cell, we construct topologically trivial and nontrivial flat bands, where both the real and imaginary parts of energy bands become flat and coalesce into a single band. We show the nontrivial systems are able to support topological boundary modes isolated from the flat bulk bands although there is no band gap. The elusive topology of flat bands can be geometrically visualized by plotting the trajectories of their eigenvectors on Bloch sphere based on Majorana's stellar representation (MSR). Furthermore, we perform a full wave simulation and show the characteristics of flat bands, associated compact localized modes, and boundary modes are reflected from absorption spectra and field intensity profiles. The study may find potential applications in lasers, narrowband filters, and efficient light harvesting.
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