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Title: Spawning rings of exceptional points out of Dirac cones

Abstract

The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity–time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an ‘exceptional ring’ in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosedmore » by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity–time symmetric systems. In this study, our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.« less

Authors:
 [1];  [2];  [3];  [1];  [1];  [4];  [5];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics; Yale Univ., New Haven, CT (United States). Dept. of Applied Physics
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics; NEC Corporation, Tsukuba, Ibaraki (Japan). Smart Energy Research Lab.
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics; Harvard Univ., Cambridge, MA (United States). Dept. of Physics
  5. DSO National Lab. (Singapore)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1371039
Grant/Contract Number:  
SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Nature (London)
Additional Journal Information:
Journal Name: Nature (London); Journal Volume: 525; Journal Issue: 7569; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 0028-0836
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
14 SOLAR ENERGY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; solar (photovoltaic); solar (thermal); solid state lighting; phonons; thermal conductivity; thermoelectric; defects; mechanical behavior; charge transport; spin dynamics; materials and chemistry by design; optics; synthesis (novel materials); synthesis (self-assembly); synthesis (scalable processing)

Citation Formats

Zhen, Bo, Hsu, Chia Wei, Igarashi, Yuichi, Lu, Ling, Kaminer, Ido, Pick, Adi, Chua, Song-Liang, Joannopoulos, John D., and Soljačić, Marin. Spawning rings of exceptional points out of Dirac cones. United States: N. p., 2015. Web. doi:10.1038/nature14889.
Zhen, Bo, Hsu, Chia Wei, Igarashi, Yuichi, Lu, Ling, Kaminer, Ido, Pick, Adi, Chua, Song-Liang, Joannopoulos, John D., & Soljačić, Marin. Spawning rings of exceptional points out of Dirac cones. United States. https://doi.org/10.1038/nature14889
Zhen, Bo, Hsu, Chia Wei, Igarashi, Yuichi, Lu, Ling, Kaminer, Ido, Pick, Adi, Chua, Song-Liang, Joannopoulos, John D., and Soljačić, Marin. Wed . "Spawning rings of exceptional points out of Dirac cones". United States. https://doi.org/10.1038/nature14889. https://www.osti.gov/servlets/purl/1371039.
@article{osti_1371039,
title = {Spawning rings of exceptional points out of Dirac cones},
author = {Zhen, Bo and Hsu, Chia Wei and Igarashi, Yuichi and Lu, Ling and Kaminer, Ido and Pick, Adi and Chua, Song-Liang and Joannopoulos, John D. and Soljačić, Marin},
abstractNote = {The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity–time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an ‘exceptional ring’ in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity–time symmetric systems. In this study, our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.},
doi = {10.1038/nature14889},
journal = {Nature (London)},
number = 7569,
volume = 525,
place = {United States},
year = {2015},
month = {9}
}

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journal, September 2018

  • Zhou, Xingping; Gupta, Samit Kumar; Huang, Zhong
  • Applied Physics Letters, Vol. 113, Issue 10
  • DOI: 10.1063/1.5043279

Angle-Resolved Thermal Emission Spectroscopy Characterization of Non-Hermitian Metacrystals
journal, January 2020


Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
journal, January 2017


Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion
journal, March 2017


Edge States and Topological Invariants of Non-Hermitian Systems
journal, August 2018


Classification of Exceptional Points and Non-Hermitian Topological Semimetals
journal, August 2019


Tuning the Effective P T Phase of Plasmonic Eigenmodes
journal, November 2019


Nonconservative Coupling in a Passive Silicon Microring Resonator
journal, January 2020


Dynamically Encircling Exceptional Points: In situ Control of Encircling Loops and the Role of the Starting Point
journal, June 2018


Topological photonics
journal, March 2019


Exceptional cones in 4D parameter space
journal, January 2020

  • Wang, Qiang; Ding, Kun; Liu, Hui
  • Optics Express, Vol. 28, Issue 2
  • DOI: 10.1364/oe.381700

Realization of complex conjugate media using non-PT-symmetric photonic crystals
journal, December 2019


How to Compute Spectra with Error Control.
text, January 2019

  • Colbrook, Matthew; Roman, Bogdan; Hansen, Anders
  • Apollo - University of Cambridge Repository
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PT symmetry in a fractional Schrödinger equation: PT symmetry in a fractional Schrödinger equation
journal, April 2016

  • Zhang, Yiqi; Zhong, Hua; Belić, Milivoj R.
  • Laser & Photonics Reviews, Vol. 10, Issue 3
  • DOI: 10.1002/lpor.201600037

Majorana bound states from exceptional points in non-topological superconductors
journal, February 2016

  • San-Jose, Pablo; Cayao, Jorge; Prada, Elsa
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep21427

Chiral-symmetry protected exceptional torus in correlated nodal-line semimetals
journal, September 2019


How to Compute Spectra with Error Control
journal, June 2019


Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
conference, January 2018

  • Cerjan, Alexander; Xiao, Meng; Yuan, Luqi
  • CLEO: QELS_Fundamental Science, Conference on Lasers and Electro-Optics
  • DOI: 10.1364/cleo_qels.2018.fm2q.4

Non-Hermitian optics in atomic systems
journal, March 2018

  • Zhang, Zhaoyang; Ma, Danmeng; Sheng, Jiteng
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 51, Issue 7
  • DOI: 10.1088/1361-6455/aaaf9f

Exceptional rings protected by emergent symmetry for mechanical systems
journal, August 2019


Non-Hermitian systems and topology: A transfer-matrix perspective
journal, June 2019


Demonstration of a two-dimensional $${\cal P}{\cal T}$$ P T -symmetric crystal
journal, January 2019


Parity-time symmetry in periodically curved optical waveguides
journal, January 2018

  • Zhang, Yan-Rong; Zhang, Ze-Zheng; Yuan, Jia-Qi
  • Optics Express, Vol. 26, Issue 21
  • DOI: 10.1364/oe.26.027141

Majorana bound states from exceptional points in non-topological superconductors
text, January 2014


General Theory of Spontaneous Emission Near Exceptional Points
text, January 2016


On-chip all-dielectric fabrication-tolerant zero-index metamaterials
text, January 2016


Dynamically encircling exceptional points: Exact evolution and polarization state conversion
text, January 2017


Photonic Topological Insulating Phase Induced Solely by Gain and Loss
text, January 2017


Parity-Time Symmetry in Non-Hermitian Complex Optical Media
text, January 2018


Symmetry and Topology in Non-Hermitian Physics
text, January 2018


Quantum state tomography across the exceptional point in a single dissipative qubit
text, January 2019


Classification of Exceptional Points and Non-Hermitian Topological Semimetals
text, January 2019


Non-Hermitian skin effect and chiral damping in open quantum systems
text, January 2019


Exceptional rings protected by emergent symmetry for mechanical systems
text, January 2019


Non-Hermitian Topological Invariants in Real Space
text, January 2019


Topological Phase Transition Independent of System Non-Hermiticity
text, January 2019


Inversion symmetric non-Hermitian Chern insulator
text, January 2019


Realization of complex conjugate media using non-PT-symmetric photonic crystals
text, January 2019


Generalized bulk-edge correspondence for non-hermitian topological systems
text, January 2019


Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains
journal, December 2016

  • Kim, Kyoung-Ho; Hwang, Min-Soo; Kim, Ha-Reem
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms13893

Parity-time-symmetric quantum critical phenomena
journal, June 2017

  • Ashida, Yuto; Furukawa, Shunsuke; Ueda, Masahito
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15791

Statistical parity-time-symmetric lasing in an optical fibre network
journal, November 2017

  • Jahromi, Ali K.; Hassan, Absar U.; Christodoulides, Demetrios N.
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/s41467-017-00958-x

Non-Hermitian photonics promises exceptional topology of light
journal, July 2018


Robust lasing modes in coupled colloidal quantum dot microdisk pairs using a non-Hermitian exceptional point
journal, February 2019


Crossing exceptional points without phase transition
journal, January 2019


Majorana bound states from exceptional points in non-topological superconductors
journal, February 2016

  • San-Jose, Pablo; Cayao, Jorge; Prada, Elsa
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep21427

Acceleration toward polarization singularity inspired by relativistic E×B drift
journal, November 2016

  • Yu, Sunkyu; Piao, Xianji; Park, Namkyoo
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep37754

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states
journal, December 2016

  • Afzal, Muhammad Imran; Lee, Yong Tak
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep39016

Manipulation of Dirac Cones in Mechanical Graphene
text, January 2015


Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
text, January 2018