$$\mathcal{PT}$$-Symmetric Topological Edge-Gain Effect
Abstract
In this work, we demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped subsystems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.
- Authors:
-
[1];
[1];
[1];
[1];
- Stanford Univ., CA (United States)
- Technion-Israel Institute of Technology, Haifa (Israel)
- Publication Date:
- Research Org.:
- Univ. of California, Oakland, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); US Air Force Office of Scientific Research (AFOSR); USDOD, Joint Directed Energy Transition Office
- OSTI Identifier:
- 1803756
- Grant/Contract Number:
- SC0019380; FA9550-17-1-0002; N00014-17-1-3030; N00014-17-1-2557
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 125; Journal Issue: 3; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Physics
Citation Formats
Song, Alex Y., Sun, Xiao-Qi, Dutt, Avik, Minkov, Momchil, Wojcik, Casey, Wang, Haiwen, Williamson, Ian A. D., Orenstein, Meir, and Fan, Shanhui. $\mathcal{PT}$-Symmetric Topological Edge-Gain Effect. United States: N. p., 2020.
Web. doi:10.1103/physrevlett.125.033603.
Song, Alex Y., Sun, Xiao-Qi, Dutt, Avik, Minkov, Momchil, Wojcik, Casey, Wang, Haiwen, Williamson, Ian A. D., Orenstein, Meir, & Fan, Shanhui. $\mathcal{PT}$-Symmetric Topological Edge-Gain Effect. United States. https://doi.org/10.1103/physrevlett.125.033603
Song, Alex Y., Sun, Xiao-Qi, Dutt, Avik, Minkov, Momchil, Wojcik, Casey, Wang, Haiwen, Williamson, Ian A. D., Orenstein, Meir, and Fan, Shanhui. Tue .
"$\mathcal{PT}$-Symmetric Topological Edge-Gain Effect". United States. https://doi.org/10.1103/physrevlett.125.033603. https://www.osti.gov/servlets/purl/1803756.
@article{osti_1803756,
title = {$\mathcal{PT}$-Symmetric Topological Edge-Gain Effect},
author = {Song, Alex Y. and Sun, Xiao-Qi and Dutt, Avik and Minkov, Momchil and Wojcik, Casey and Wang, Haiwen and Williamson, Ian A. D. and Orenstein, Meir and Fan, Shanhui},
abstractNote = {In this work, we demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped subsystems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.},
doi = {10.1103/physrevlett.125.033603},
journal = {Physical Review Letters},
number = 3,
volume = 125,
place = {United States},
year = {Tue Jul 14 00:00:00 EDT 2020},
month = {Tue Jul 14 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Anomalous helical edge states in a non-Hermitian Chern insulator
journal, October 2018
- Kawabata, Kohei; Shiozaki, Ken; Ueda, Masahito
- Physical Review B, Vol. 98, Issue 16
Topological insulators and superconductors
journal, October 2011
- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Reviews of Modern Physics, Vol. 83, Issue 4
The Quantum Spin Hall Effect
journal, March 2011
- Maciejko, Joseph; Hughes, Taylor L.; Zhang, Shou-Cheng
- Annual Review of Condensed Matter Physics, Vol. 2, Issue 1
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
journal, July 2018
- Kunst, Flore K.; Edvardsson, Elisabet; Budich, Jan Carl
- Physical Review Letters, Vol. 121, Issue 2
Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries
journal, August 2002
- Mostafazadeh, Ali
- Journal of Mathematical Physics, Vol. 43, Issue 8
Stable topological edge states in a non-Hermitian four-band model
journal, July 2018
- Yuce, C.
- Physical Review A, Vol. 98, Issue 1
Quantum spin Hall effect of light
journal, June 2015
- Bliokh, K. Y.; Smirnova, D.; Nori, F.
- Science, Vol. 348, Issue 6242
Photonic Topological Insulating Phase Induced Solely by Gain and Loss
journal, November 2018
- Takata, Kenta; Notomi, Masaya
- Physical Review Letters, Vol. 121, Issue 21
Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007
- Konig, M.; Wiedmann, S.; Brune, C.
- Science, Vol. 318, Issue 5851, p. 766-770
Topological Phases of Non-Hermitian Systems
journal, September 2018
- Gong, Zongping; Ashida, Yuto; Kawabata, Kohei
- Physical Review X, Vol. 8, Issue 3
Anti–parity-time symmetry in diffusive systems
journal, April 2019
- Li, Ying; Peng, Yu-Gui; Han, Lei
- Science, Vol. 364, Issue 6436
Electromagnetic Impurity-Immunity Induced by Parity-Time Symmetry
journal, August 2018
- Luo, Jie; Li, Jensen; Lai, Yun
- Physical Review X, Vol. 8, Issue 3
Topological photonic crystal nanocavity laser
journal, November 2018
- Ota, Yasutomo; Katsumi, Ryota; Watanabe, Katsuyuki
- Communications Physics, Vol. 1, Issue 1
Topological states in photonic systems
journal, June 2016
- Lu, Ling; Joannopoulos, John D.; Soljačić, Marin
- Nature Physics, Vol. 12, Issue 7
Measurement of topological invariants in a 2D photonic system
journal, February 2016
- Mittal, Sunil; Ganeshan, Sriram; Fan, Jingyun
- Nature Photonics, Vol. 10, Issue 3
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006
- Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C.
- Science, Vol. 314, Issue 5806, p. 1757-1761
Edge-Mode Lasing in 1D Topological Active Arrays
journal, March 2018
- Parto, Midya; Wittek, Steffen; Hodaei, Hossein
- Physical Review Letters, Vol. 120, Issue 11
Real Spectra in Non-Hermitian Hamiltonians Having Symmetry
journal, June 1998
- Bender, Carl M.; Boettcher, Stefan
- Physical Review Letters, Vol. 80, Issue 24
Temporal coupled-mode theory for the Fano resonance in optical resonators
journal, January 2003
- Fan, Shanhui; Suh, Wonjoo; Joannopoulos, J. D.
- Journal of the Optical Society of America A, Vol. 20, Issue 3
Robust optical delay lines with topological protection
journal, August 2011
- Hafezi, Mohammad; Demler, Eugene A.; Lukin, Mikhail D.
- Nature Physics, Vol. 7, Issue 11
A topological quantum optics interface
journal, February 2018
- Barik, Sabyasachi; Karasahin, Aziz; Flower, Christopher
- Science, Vol. 359, Issue 6376
Topologically protected bound states in photonic parity–time-symmetric crystals
journal, December 2016
- Weimann, S.; Kremer, M.; Plotnik, Y.
- Nature Materials, Vol. 16, Issue 4
Edge states at the interface of non-Hermitian systems
journal, April 2018
- Yuce, C.
- Physical Review A, Vol. 97, Issue 4
Photonic topological insulators
journal, December 2012
- Khanikaev, Alexander B.; Hossein Mousavi, S.; Tse, Wang-Kong
- Nature Materials, Vol. 12, Issue 3
Lasing in topological edge states of a one-dimensional lattice
journal, September 2017
- St-Jean, P.; Goblot, V.; Galopin, E.
- Nature Photonics, Vol. 11, Issue 10
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
journal, January 2017
- Leykam, Daniel; Bliokh, Konstantin Y.; Huang, Chunli
- Physical Review Letters, Vol. 118, Issue 4
Topological photonics
journal, October 2014
- Lu, Ling; Joannopoulos, John D.; Soljačić, Marin
- Nature Photonics, Vol. 8, Issue 11
Two-dimensional topological photonics
journal, November 2017
- Khanikaev, Alexander B.; Shvets, Gennady
- Nature Photonics, Vol. 11, Issue 12
Edge States and Topological Invariants of Non-Hermitian Systems
journal, August 2018
- Yao, Shunyu; Wang, Zhong
- Physical Review Letters, Vol. 121, Issue 8
Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities
journal, October 2004
- Wonjoo Suh,
- IEEE Journal of Quantum Electronics, Vol. 40, Issue 10
PT symmetry protected non-Hermitian topological systems
journal, November 2018
- Yuce, C.; Oztas, Z.
- Scientific Reports, Vol. 8, Issue 1
Two-Dimensional Topological Polariton Laser
journal, February 2019
- Kartashov, Yaroslav V.; Skryabin, Dmitry V.
- Physical Review Letters, Vol. 122, Issue 8
The non-equivalence of pseudo-Hermiticity and presence of antilinear symmetry
journal, August 2009
- Siegl, Petr
- Pramana, Vol. 73, Issue 2
PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability
journal, January 2020
- Zhang, Ruili; Qin, Hong; Xiao, Jianyuan
- Journal of Mathematical Physics, Vol. 61, Issue 1
Topological invariance and global Berry phase in non-Hermitian systems
journal, January 2013
- Liang, Shi-Dong; Huang, Guang-Yao
- Physical Review A, Vol. 87, Issue 1
Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
journal, January 2008
- Haldane, F. D. M.; Raghu, S.
- Physical Review Letters, Vol. 100, Issue 1
Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies
journal, November 2012
- Feng, Liang; Xu, Ye-Long; Fegadolli, William S.
- Nature Materials, Vol. 12, Issue 2
-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems
journal, March 2011
- Chong, Y. D.; Ge, Li; Stone, A. Douglas
- Physical Review Letters, Vol. 106, Issue 9
Observation of -Symmetry Breaking in Complex Optical Potentials
journal, August 2009
- Guo, A.; Salamo, G. J.; Duchesne, D.
- Physical Review Letters, Vol. 103, Issue 9
Topological photonics
journal, March 2019
- Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto
- Reviews of Modern Physics, Vol. 91, Issue 1
All-real spectra in optical systems with arbitrary gain-and-loss distributions
journal, March 2016
- Nixon, Sean; Yang, Jianke
- Physical Review A, Vol. 93, Issue 3
Spin-Orbit Coupling and the Optical Spin Hall Effect in Photonic Graphene
journal, January 2015
- Nalitov, A. V.; Malpuech, G.; Terças, H.
- Physical Review Letters, Vol. 114, Issue 2
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
journal, August 1982
- Thouless, D. J.; Kohmoto, M.; Nightingale, M. P.
- Physical Review Letters, Vol. 49, Issue 6
Symmetry and Topology in Non-Hermitian Physics
journal, October 2019
- Kawabata, Kohei; Shiozaki, Ken; Ueda, Masahito
- Physical Review X, Vol. 9, Issue 4
Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
journal, July 2018
- Dangel, Felix; Wagner, Marcel; Cartarius, Holger
- Physical Review A, Vol. 98, Issue 1
Hall Effect of Light
journal, August 2004
- Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto
- Physical Review Letters, Vol. 93, Issue 8
Single-mode laser by parity-time symmetry breaking
journal, October 2014
- Feng, L.; Wong, Z. J.; Ma, R. -M.
- Science, Vol. 346, Issue 6212
Topological Order and the Quantum Spin Hall Effect
journal, September 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 14, Article No. 146802
Photonic Floquet topological insulators
journal, April 2013
- Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan
- Nature, Vol. 496, Issue 7444
Topological hybrid silicon microlasers
journal, March 2018
- Zhao, Han; Miao, Pei; Teimourpour, Mohammad H.
- Nature Communications, Vol. 9, Issue 1
Observation of parity–time symmetry in optics
journal, January 2010
- Rüter, Christian E.; Makris, Konstantinos G.; El-Ganainy, Ramy
- Nature Physics, Vol. 6, Issue 3
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
Quantum Spin Hall Effect in Graphene
journal, November 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 22
Parity–time symmetry and exceptional points in photonics
journal, April 2019
- Özdemir, Ş. K.; Rotter, S.; Nori, F.
- Nature Materials, Vol. 18, Issue 8
Non-Hermitian Gauged Topological Laser Arrays
journal, May 2018
- Longhi, Stefano
- Annalen der Physik, Vol. 530, Issue 7
Topological insulator laser: Theory
journal, February 2018
- Harari, Gal; Bandres, Miguel A.; Lumer, Yaakov
- Science, Vol. 359, Issue 6381
Imaging topological edge states in silicon photonics
journal, October 2013
- Hafezi, M.; Mittal, S.; Fan, J.
- Nature Photonics, Vol. 7, Issue 12
Optical Resonator Analog of a Two-Dimensional Topological Insulator
journal, May 2013
- Liang, G. Q.; Chong, Y. D.
- Physical Review Letters, Vol. 110, Issue 20
Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
journal, January 2019
- Kawabata, Kohei; Higashikawa, Sho; Gong, Zongping
- Nature Communications, Vol. 10, Issue 1
Absence of topological insulator phases in non-Hermitian -symmetric Hamiltonians
journal, October 2011
- Hu, Yi Chen; Hughes, Taylor L.
- Physical Review B, Vol. 84, Issue 15
Parity-time-symmetric microring lasers
journal, October 2014
- Hodaei, H.; Miri, M. -A.; Heinrich, M.
- Science, Vol. 346, Issue 6212
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988
- Haldane, F. D. M.
- Physical Review Letters, Vol. 61, Issue 18
Nonreciprocal lasing in topological cavities of arbitrary geometries
journal, October 2017
- Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe
- Science, Vol. 358, Issue 6363
Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy
journal, July 2014
- Ge, Li; Stone, A. Douglas
- Physical Review X, Vol. 4, Issue 3
Topological insulator laser: Experiments
journal, February 2018
- Bandres, Miguel A.; Wittek, Steffen; Harari, Gal
- Science, Vol. 359, Issue 6381
Realization of a three-dimensional photonic topological insulator
journal, January 2019
- Yang, Yihao; Gao, Zhen; Xue, Haoran
- Nature, Vol. 565, Issue 7741
A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension
journal, October 2018
- Lin, Qian; Sun, Xiao-Qi; Xiao, Meng
- Science Advances, Vol. 4, Issue 10
Chern number and edge states in the integer quantum Hall effect
journal, November 1993
- Hatsugai, Yasuhiro
- Physical Review Letters, Vol. 71, Issue 22
Beam Dynamics in Symmetric Optical Lattices
journal, March 2008
- Makris, K. G.; El-Ganainy, R.; Christodoulides, D. N.
- Physical Review Letters, Vol. 100, Issue 10
Topologically protected midgap states in complex photonic lattices
journal, January 2013
- Schomerus, Henning
- Optics Letters, Vol. 38, Issue 11
Observation of unidirectional backscattering-immune topological electromagnetic states
journal, October 2009
- Wang, Zheng; Chong, Yidong; Joannopoulos, J. D.
- Nature, Vol. 461, Issue 7265
Edge states and topological phases in non-Hermitian systems
journal, November 2011
- Esaki, Kenta; Sato, Masatoshi; Hasebe, Kazuki
- Physical Review B, Vol. 84, Issue 20
Topologically Protected Defect States in Open Photonic Systems with Non-Hermitian Charge-Conjugation and Parity-Time Symmetry
journal, November 2015
- Malzard, Simon; Poli, Charles; Schomerus, Henning
- Physical Review Letters, Vol. 115, Issue 20
Topological Waveguiding near an Exceptional Point: Defect-Immune, Slow-Light, and Loss-Immune Propagation
journal, August 2018
- Hassani Gangaraj, S. Ali; Monticone, Francesco
- Physical Review Letters, Vol. 121, Issue 9
Topological Phase Transitions in the Photonic Spin Hall Effect
journal, October 2017
- Kort-Kamp, W. J. M.
- Physical Review Letters, Vol. 119, Issue 14
Demonstration of a two-dimensional $${\cal P}{\cal T}$$ P T -symmetric crystal
journal, January 2019
- Kremer, Mark; Biesenthal, Tobias; Maczewsky, Lukas J.
- Nature Communications, Vol. 10, Issue 1