$$\mathcal{PT}$$-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:
-
- 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}
}
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