Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media

Fu, Yichen; Qin, Hong

doi:10.1103/PhysRevResearch.6.023273

Title: Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media

Journal Article · 13 June 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.023273 · OSTI ID:2474384

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In classical Hermitian continuous media, the spectral-flow index of topological modes is linked to the bulk topology via index theorem. However, the interface between two bulks is usually non-Hermitian due to the inhomogeneities of system parameters. We show that the connection between topological modes and bulk topology still exists despite the non-Hermiticity at the interface if the system is endowed with PT symmetry. The theoretical framework developed is applied to the Hall magnetohydrodynamic model to identify a topological mode called topological Alfvén sound wave in magnetized plasmas. Published by the American Physical Society 2024

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2474384

Report Number(s):: LLNL-JRNL-863977; 023273

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 6; ISSN PPRHAI; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (70)

Anti- (conjugate) linearity Uhlmann, Armin Science China Physics, Mechanics & Astronomy, Vol. 59, Issue 3 https://doi.org/10.1007/s11433-015-5777-1	journal	January 2016
Distribution functions in physics: Fundamentals Hillery, M.; O'Connell, R. F.; Scully, M. O. Physics Reports, Vol. 106, Issue 3 https://doi.org/10.1016/0370-1573(84)90160-1	journal	April 1984
Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas Goedbloed, J. P. Hans; Poedts, Stefaan https://doi.org/10.1017/CBO9780511616945	book	February 2010
Ideal MHD Freidberg, Jeffrey P. https://doi.org/10.1017/CBO9780511795046	book	July 2014
The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas Fu, Yichen; Qin, Hong Journal of Plasma Physics, Vol. 88, Issue 4 https://doi.org/10.1017/S0022377822000629	journal	July 2022
Quantum mechanics as a statistical theory Moyal, J. E. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 45, Issue 1 https://doi.org/10.1017/S0305004100000487	journal	January 1949
Physics of Nonhermitian Degeneracies Berry, M. V. Czechoslovak Journal of Physics, Vol. 54, Issue 10 https://doi.org/10.1023/B:CJOP.0000044002.05657.04	journal	October 2004
Type-II Weyl semimetals Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun Nature, Vol. 527, Issue 7579 https://doi.org/10.1038/nature15768	journal	November 2015
Photonic Weyl degeneracies in magnetized plasma Gao, Wenlong; Yang, Biao; Lawrence, Mark Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12435	journal	August 2016
Non-Hermitian physics and PT symmetry El-Ganainy, Ramy; Makris, Konstantinos G.; Khajavikhan, Mercedeh Nature Physics, Vol. 14, Issue 1 https://doi.org/10.1038/nphys4323	journal	January 2018
Topological phases and bulk-edge correspondence of magnetized cold plasmas Fu, Yichen; Qin, Hong Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-24189-3	journal	June 2021
Parity–time symmetry and exceptional points in photonics Özdemir, Ş. K.; Rotter, S.; Nori, F. Nature Materials, Vol. 18, Issue 8 https://doi.org/10.1038/s41563-019-0304-9	journal	April 2019
Experimental realization of a Weyl exceptional ring Cerjan, Alexander; Huang, Sheng; Wang, Mohan Nature Photonics, Vol. 13, Issue 9 https://doi.org/10.1038/s41566-019-0453-z	journal	June 2019
Topological transition in stratified fluids Perrot, Manolis; Delplace, Pierre; Venaille, Antoine Nature Physics, Vol. 15, Issue 8 https://doi.org/10.1038/s41567-019-0561-1	journal	June 2019
Linear stability of static equilibrium states in the Hall-magnetohydrodynamics model Hameiri, Eliezer; Torasso, R. Physics of Plasmas, Vol. 11, Issue 11 https://doi.org/10.1063/1.1784453	journal	November 2004
Waves in the Hall-magnetohydrodynamics model Hameiri, Eliezer; Ishizawa, Akihiro; Ishida, Akio Physics of Plasmas, Vol. 12, Issue 7 https://doi.org/10.1063/1.1952887	journal	July 2005
Periodic table for topological insulators and superconductors Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings https://doi.org/10.1063/1.3149495	conference	January 2009
Kelvin-Helmholtz instability is the result of parity-time symmetry breaking Qin, Hong; Zhang, Ruili; Glasser, Alexander S. Physics of Plasmas, Vol. 26, Issue 3 https://doi.org/10.1063/1.5088498	journal	March 2019
PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability Zhang, Ruili; Qin, Hong; Xiao, Jianyuan Journal of Mathematical Physics, Vol. 61, Issue 1 https://doi.org/10.1063/1.5117211	journal	January 2020
Making sense of non-Hermitian Hamiltonians Bender, Carl M. Reports on Progress in Physics, Vol. 70, Issue 6 https://doi.org/10.1088/0034-4885/70/6/R03	journal	May 2007
The physics of spontaneous parity-time symmetry breaking in the Kelvin–Helmholtz instability Fu, Yichen; Qin, Hong New Journal of Physics, Vol. 22, Issue 8 https://doi.org/10.1088/1367-2630/aba38f	journal	August 2020
The physics of exceptional points Heiss, W. D. Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 44 https://doi.org/10.1088/1751-8113/45/44/444016	journal	October 2012
Topological physics of non-Hermitian optics and photonics: a review Wang, Hongfei; Zhang, Xiujuan; Hua, Jinguo Journal of Optics, Vol. 23, Issue 12 https://doi.org/10.1088/2040-8986/ac2e15	journal	October 2021
Why does bulk boundary correspondence fail in some non-hermitian topological models Xiong, Ye Journal of Physics Communications, Vol. 2, Issue 3 https://doi.org/10.1088/2399-6528/aab64a	journal	March 2018
Chiral Maxwell waves in continuous media from Berry monopoles Marciani, M.; Delplace, P. Physical Review A, Vol. 101, Issue 2 https://doi.org/10.1103/PhysRevA.101.023827	journal	February 2020
Analogs of quantum-Hall-effect edge states in photonic crystals Raghu, S.; Haldane, F. D. M. Physical Review A, Vol. 78, Issue 3 https://doi.org/10.1103/PhysRevA.78.033834	journal	September 2008
Topological response in Weyl semimetals and the chiral anomaly Zyuzin, A. A.; Burkov, A. A. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115133	journal	September 2012
Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges Cerjan, Alexander; Xiao, Meng; Yuan, Luqi Physical Review B, Vol. 97, Issue 7 https://doi.org/10.1103/PhysRevB.97.075128	journal	February 2018
Photon topology Palmerduca, Eric; Qin, Hong Physical Review D, Vol. 109, Issue 8 https://doi.org/10.1103/PhysRevD.109.085005	journal	April 2024
Spontaneous and explicit parity-time-symmetry breaking in drift-wave instabilities Qin, Hong; Fu, Yichen; Glasser, Alexander S. Physical Review E, Vol. 104, Issue 1 https://doi.org/10.1103/PhysRevE.104.015215	journal	July 2021
Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry Haldane, F. D. M.; Raghu, S. Physical Review Letters, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevLett.100.013904	journal	January 2008
Topological Phonon Modes and Their Role in Dynamic Instability of Microtubules Prodan, Emil; Prodan, Camelia Physical Review Letters, Vol. 103, Issue 24 https://doi.org/10.1103/PhysRevLett.103.248101	journal	December 2009
Topological Nature of the Phonon Hall Effect Zhang, Lifa; Ren, Jie; Wang, Jian-Sheng Physical Review Letters, Vol. 105, Issue 22 https://doi.org/10.1103/PhysRevLett.105.225901	journal	November 2010
Topological Acoustics Yang, Zhaoju; Gao, Fei; Shi, Xihang Physical Review Letters, Vol. 114, Issue 11 https://doi.org/10.1103/PhysRevLett.114.114301	journal	March 2015
Topological Phononic Crystals with One-Way Elastic Edge Waves Wang, Pai; Lu, Ling; Bertoldi, Katia Physical Review Letters, Vol. 115, Issue 10 https://doi.org/10.1103/PhysRevLett.115.104302	journal	September 2015
Anomalous Edge State in a Non-Hermitian Lattice Lee, Tony E. Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/PhysRevLett.116.133903	journal	April 2016
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems Leykam, Daniel; Bliokh, Konstantin Y.; Huang, Chunli Physical Review Letters, Vol. 118, Issue 4 https://doi.org/10.1103/PhysRevLett.118.040401	journal	January 2017
Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas Xu, Yong; Wang, Sheng-Tao; Duan, L. -M. Physical Review Letters, Vol. 118, Issue 4 https://doi.org/10.1103/PhysRevLett.118.045701	journal	January 2017
Topological Band Theory for Non-Hermitian Hamiltonians Shen, Huitao; Zhen, Bo; Fu, Liang Physical Review Letters, Vol. 120, Issue 14 https://doi.org/10.1103/PhysRevLett.120.146402	journal	April 2018
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems Kunst, Flore K.; Edvardsson, Elisabet; Budich, Jan Carl Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/PhysRevLett.121.026808	journal	July 2018
Edge States and Topological Invariants of Non-Hermitian Systems Yao, Shunyu; Wang, Zhong Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.086803	journal	August 2018
Non-Hermitian Chern Bands Yao, Shunyu; Song, Fei; Wang, Zhong Physical Review Letters, Vol. 121, Issue 13 https://doi.org/10.1103/PhysRevLett.121.136802	journal	September 2018
Topological Waves in Fluids with Odd Viscosity Souslov, Anton; Dasbiswas, Kinjal; Fruchart, Michel Physical Review Letters, Vol. 122, Issue 12 https://doi.org/10.1103/PhysRevLett.122.128001	journal	March 2019
Classification of Exceptional Points and Non-Hermitian Topological Semimetals Kawabata, Kohei; Bessho, Takumi; Sato, Masatoshi Physical Review Letters, Vol. 123, Issue 6 https://doi.org/10.1103/PhysRevLett.123.066405	journal	August 2019
Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems Song, Fei; Yao, Shunyu; Wang, Zhong Physical Review Letters, Vol. 123, Issue 17 https://doi.org/10.1103/PhysRevLett.123.170401	journal	October 2019
Topological Origin of Non-Hermitian Skin Effects Okuma, Nobuyuki; Kawabata, Kohei; Shiozaki, Ken Physical Review Letters, Vol. 124, Issue 8 https://doi.org/10.1103/PhysRevLett.124.086801	journal	February 2020
Topological Gaseous Plasmon Polariton in Realistic Plasma Parker, Jeffrey B.; Marston, J. B.; Tobias, Steven M. Physical Review Letters, Vol. 124, Issue 19 https://doi.org/10.1103/PhysRevLett.124.195001	journal	May 2020
Unidirectional Modes Induced by Nontraditional Coriolis Force in Stratified Fluids Perez, Nicolas; Delplace, Pierre; Venaille, Antoine Physical Review Letters, Vol. 128, Issue 18 https://doi.org/10.1103/PhysRevLett.128.184501	journal	May 2022
Non-Hermitian Spectral Flows and Berry-Chern Monopoles Jezequel, Lucien; Delplace, Pierre Physical Review Letters, Vol. 130, Issue 6 https://doi.org/10.1103/PhysRevLett.130.066601	journal	February 2023
Quantized Hall Conductance in a Two-Dimensional Periodic Potential Thouless, D. J.; Kohmoto, M.; Nightingale, M. P. Physical Review Letters, Vol. 49, Issue 6 https://doi.org/10.1103/PhysRevLett.49.405	journal	August 1982
Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase Simon, Barry Physical Review Letters, Vol. 51, Issue 24 https://doi.org/10.1103/PhysRevLett.51.2167	journal	December 1983
Real Spectra in Non-Hermitian Hamiltonians Having P T Symmetry Bender, Carl M.; Boettcher, Stefan Physical Review Letters, Vol. 80, Issue 24 https://doi.org/10.1103/PhysRevLett.80.5243	journal	June 1998
Topology of rotating stratified fluids with and without background shear flow Zhu, Ziyan; Li, Christopher; Marston, J. B. Physical Review Research, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevResearch.5.033191	journal	September 2023
Topological Phases of Non-Hermitian Systems Gong, Zongping; Ashida, Yuto; Kawabata, Kohei Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031079	journal	September 2018
Symmetry and Topology in Non-Hermitian Physics Kawabata, Kohei; Shiozaki, Ken; Ueda, Masahito Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041015	journal	October 2019
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Classification of topological quantum matter with symmetries Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P. Reviews of Modern Physics, Vol. 88, Issue 3 https://doi.org/10.1103/RevModPhys.88.035005	journal	August 2016
Weyl and Dirac semimetals in three-dimensional solids Armitage, N. P.; Mele, E. J.; Vishwanath, Ashvin Reviews of Modern Physics, Vol. 90, Issue 1 https://doi.org/10.1103/RevModPhys.90.015001	journal	January 2018
Topological photonics Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto Reviews of Modern Physics, Vol. 91, Issue 1 https://doi.org/10.1103/RevModPhys.91.015006	journal	March 2019
Exceptional topology of non-Hermitian systems Bergholtz, Emil J.; Budich, Jan Carl; Kunst, Flore K. Reviews of Modern Physics, Vol. 93, Issue 1 https://doi.org/10.1103/RevModPhys.93.015005	journal	February 2021
Topological Langmuir-cyclotron wave Qin, Hong; Fu, Yichen Science Advances, Vol. 9, Issue 13 https://doi.org/10.1126/sciadv.add8041	journal	March 2023
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C. Science, Vol. 314, Issue 5806, p. 1757-1761 https://doi.org/10.1126/science.1133734	journal	December 2006
Topological origin of equatorial waves Delplace, Pierre; Marston, J. B.; Venaille, Antoine Science, Vol. 358, Issue 6366 https://doi.org/10.1126/science.aan8819	journal	October 2017
Exceptional points in optics and photonics Miri, Mohammad-Ali; Alù, Andrea Science, Vol. 363, Issue 6422 https://doi.org/10.1126/science.aar7709	journal	January 2019
Non-Hermitian Topological Phenomena: A Review Okuma, Nobuyuki; Sato, Masatoshi Annual Review of Condensed Matter Physics, Vol. 14, Issue 1 https://doi.org/10.1146/annurev-conmatphys-040521-033133	journal	March 2023
A gauge theory for shallow water Tong, David SciPost Physics, Vol. 14, Issue 5 https://doi.org/10.21468/SciPostPhys.14.5.102	journal	May 2023
An introduction to spontaneous symmetry breaking Beekman, Aron; Rademaker, Louk; van Wezel, Jasper SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.11	journal	December 2019
Berry-Chern monopoles and spectral flows Delplace, Pierre SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.39	journal	March 2022
Manifestation of the topological index formula in quantum waves and geophysical waves Faure, Frédéric Annales Henri Lebesgue, Vol. 6 https://doi.org/10.5802/ahl.169	journal	July 2023