Multimode One-Way Waveguides of Large Chern Numbers

Skirlo, Scott A.; Lu, Ling; Soljačić, Marin

doi:10.1103/PhysRevLett.113.113904

Title: Multimode One-Way Waveguides of Large Chern Numbers

Abstract

Current experimental realizations of the quantum anomalous Hall phase in both electronic and photonic systems have been limited to a Chern number of one. In photonics, this corresponds to a single-mode one-way edge waveguide. We predict quantum anomalous Hall phases in photonic crystals with large Chern numbers of 2, 3, and 4. These new topological phases were found by simultaneously gapping multiple Dirac and quadratic points. We demonstrate a continuously tunable power splitter as a possible application of multimode one-way waveguides. All our findings are readily realizable at microwave frequencies.

Authors:

Skirlo, Scott A. ^[1]; Lu, Ling ^[1]; Soljačić, Marin ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics

Publication Date:: Fri Sep 12 00:00:00 EDT 2014

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); 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); National Science Foundation (NSF); US Army Research Office (ARO)

OSTI Identifier:: 1210647

Alternate Identifier(s):: OSTI ID: 1180423

Grant/Contract Number:: SC0001299; FG02-09ER46577; DMR-0819762; W911NF-13-D-0001

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 113; Journal Issue: 11; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Skirlo, Scott A., Lu, Ling, and Soljačić, Marin. Multimode One-Way Waveguides of Large Chern Numbers.  United States: N. p., 2014. 
Web.  doi:10.1103/PhysRevLett.113.113904.

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                    Skirlo, Scott A., Lu, Ling, & Soljačić, Marin. Multimode One-Way Waveguides of Large Chern Numbers.  United States.  https://doi.org/10.1103/PhysRevLett.113.113904

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                    Skirlo, Scott A., Lu, Ling, and Soljačić, Marin. Fri .  
"Multimode One-Way Waveguides of Large Chern Numbers".  United States.  https://doi.org/10.1103/PhysRevLett.113.113904.  https://www.osti.gov/servlets/purl/1210647.

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@article{osti_1210647,

  title        = {Multimode One-Way Waveguides of Large Chern Numbers},

  author       = {Skirlo, Scott A. and Lu, Ling and Soljačić, Marin},

  abstractNote = {Current experimental realizations of the quantum anomalous Hall phase in both electronic and photonic systems have been limited to a Chern number of one. In photonics, this corresponds to a single-mode one-way edge waveguide. We predict quantum anomalous Hall phases in photonic crystals with large Chern numbers of 2, 3, and 4. These new topological phases were found by simultaneously gapping multiple Dirac and quadratic points. We demonstrate a continuously tunable power splitter as a possible application of multimode one-way waveguides. All our findings are readily realizable at microwave frequencies.},

  doi          = {10.1103/PhysRevLett.113.113904},

  journal      = {Physical Review Letters},

  number       = 11,

  volume       = 113,

  place        = {United States},

  year         = {Fri Sep 12 00:00:00 EDT 2014},

  month        = {Fri Sep 12 00:00:00 EDT 2014}

}

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https://doi.org/10.1103/PhysRevLett.113.113904

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Cited by: 175 works

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Figures / Tables:

FIG. 1: (color online). Bulk and edge TM band structures showing two one-way edge states (C_gap = 2) obtained from four Dirac points. The photonic crystal is a square lattice of rods with a radius of 0.13a, ϵ = 13, and μ = 1. The T-breaking perturbation corresponds to addingmore »

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Topological Phononic Crystals with One-Way Elastic Edge Waves

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We report here a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novelmore »« less
Cited by 506
https://doi.org/10.1103/physrevlett.115.104302

Full Text Available
Experimental Observation of Large Chern Numbers in Photonic Crystals

Journal Article Skirlo, Scott A. ; Lu, Ling ; Igarashi, Yuichi ; ... - Physical Review Letters

Despite great interest in the quantum anomalous Hall phase and its analogs, all experimental studies in electronic and bosonic systems have been limited to a Chern number of one. In this work, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Band gaps with large Chern numbers of 2, 3, and 4 are present in the experimental results, which show excellent agreement with theory. We calculate the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations.
Cited by 159
https://doi.org/10.1103/PhysRevLett.115.253901

Full Text Available
The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

Journal Article Dubček, Tena ; Lelas, Karlo ; Jukić, Dario ; ... - New Journal of Physics

Here we propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. Lastly, we compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.
Cited by 13
https://doi.org/10.1088/1367-2630/17/12/125002

Full Text Available
Realization of multimode operators with passive linear optics and photodetection

Journal Article Clausen, J ; Knoell, L ; Welsch, D -G - Physical Review. A

A scheme is proposed for implementing a desired transformation of the unknown quantum state of a traveling optical multimode signal. The operator describing this transformation is built up as a polynomial in products of the mode operators. There is no limitation to unitary operators realized by the scheme, the implementation is conditional however, i.e., the desired operator can be realized only with a certain success probability which depends on the respective operator and the input state. While the scheme requires the preparation of single-photon and coherent states, it exclusively makes use of beam splitters and zero- and single-photon detections. Themore »« less
https://doi.org/10.1103/PhysRevA.68.043822
Tuning the Chern number in quantum anomalous Hall insulators

Journal Article Zhao, Yi-Fan ; Zhang, Ruoxi ; Mei, Ruobing ; ... - Nature (London)

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h/(Ce²) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer). The QAH effect has been realized in magnetic topological insulators and magic-angle twisted bilayer graphene. However, the QAH effect at zero magnetic field has so far been realized only for C = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C = 5) in multilayer structuresmore »« less
https://doi.org/10.1038/s41586-020-3020-3

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Title: Multimode One-Way Waveguides of Large Chern Numbers

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Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States journal, March 2011

Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides journal, May 2011

Left-handed and right-handed one-way edge modes in a gyromagnetic photonic crystal journal, June 2010

Local density of states of chiral Hall edge states in gyrotropic photonic clusters journal, July 2013

Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal journal, March 2010

One-way edge mode in a gyromagnetic photonic crystal slab journal, January 2012

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator journal, March 2013

Topological States and Adiabatic Pumping in Quasicrystals journal, September 2012

Photonic Floquet topological insulators journal, April 2013

Weyl points and line nodes in gyroid photonic crystals journal, March 2013

Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces journal, July 2010

Highly efficient photonic-crystal splitters based on one-way waveguiding journal, December 2012

Microscopic theory of photonic one-way edge mode journal, August 2011

Robust optical delay lines with topological protection journal, August 2011

Large-Chern-Number Quantum Anomalous Hall Effect in Thin-Film Topological Crystalline Insulators journal, January 2014

Realizing effective magnetic field for photons by controlling the phase of dynamic modulation journal, October 2012

Edge mode in nonreciprocal photonic crystal waveguide: manipulating the unidirectional electromagnetic pulse dynamically journal, January 2011

Photonic topological insulators journal, December 2012

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" journal, October 1988

Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances journal, June 2005

Effective theory of quadratic degeneracies journal, June 2008

Quantum Anomalous Hall Effect with Higher Plateaus journal, September 2013

Experimental demonstration of one-way slow wave in waveguide involving gyromagnetic photonic crystals journal, June 2013

Chern number and edge states in the integer quantum Hall effect journal, November 1993

Analogs of quantum-Hall-effect edge states in photonic crystals journal, September 2008

Observation of unidirectional backscattering-immune topological electromagnetic states journal, October 2009

One-way edge mode in a magneto-optical honeycomb photonic crystal journal, July 2009

Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry journal, January 2008

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal journal, January 2008

Broadband circulators based on directional coupling of one-way waveguides journal, January 2011

Photonic Floquet topological insulators conference, September 2013

Photonic Topological Insulators journal, January 2013

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal text, January 2007

Robust optical delay lines via topological protection text, January 2011

Photonic Floquet Topological Insulators text, January 2012

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator text, January 2016

Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances text, January 2005

Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry text, January 2005

Applications of Topological Photonics in Integrated Photonic Devices journal, August 2017

Thermo-optical Tunable Ultracompact Chip-Integrated 1D Photonic Topological Insulator journal, December 2017

Extremely Broadband Topological Surface States in a Photonic Topological Metamaterial journal, July 2019

Resonant Transmission through Topological Metamaterial Grating journal, August 2018

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays: Topological phase transitions and Thouless pumping of light in photonic waveguide arrays journal, October 2016

Universal numerical calculation method for the Berry curvature and Chern numbers of typical topological photonic crystals journal, January 2020

Floquet topological insulators for sound journal, June 2016

Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states journal, October 2016

Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide journal, December 2014

Topological photonics journal, October 2014

Synthetic gauge flux and Weyl points in acoustic systems journal, September 2015

Topological states in photonic systems journal, June 2016

Topological light-trapping on a dislocation journal, June 2018

Robust temporal pumping in a magneto-mechanical topological insulator journal, February 2020

Two-dimensional topological photonics journal, November 2017

The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry journal, February 2015

Dirac directional emission in anisotropic zero refractive index photonic crystals journal, August 2015

Equivalence of electric, magnetic, and electromagnetic Chern numbers for topological photonic crystals journal, February 2020

Observation of topological edge states of acoustic metamaterials at subwavelength scale journal, April 2018

Nodal-line semimetal superlattices journal, November 2018

Topological phase transition with p orbitals in the exciton-polariton honeycomb lattice journal, June 2019

Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow journal, May 2015

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale journal, July 2017

Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology journal, September 2019

One-way edge modes in truncated semiconductor photonic crystal at terahertz frequencies journal, May 2019

Ultra-subwavelength focusing and giant magnetic-field enhancement in a low-loss one-way waveguide based on remanence journal, January 2020

Floquet engineering of exotic topological phases in systems of cold atoms journal, August 2019

Topological Edge State in the Two-Dimensional Stampfli-Triangle Photonic Crystals journal, October 2019

Floquet engineering with particle swarm optimization: Maximizing topological invariants journal, December 2019

Large Chern-number topological superfluids in a coupled-layer system journal, April 2015

Towards large-Chern-number topological phases by periodic quenching journal, May 2016

Configurable Dirac-like conical dispersions in complex photonic crystals journal, January 2017

Topological phases in a Weyl semimetal multilayer journal, April 2017

Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation journal, July 2017

Observation of valleylike edge states of sound at a momentum away from the high-symmetry points journal, April 2018

Recipe for creating an arbitrary number of Floquet chiral edge states journal, June 2018

Experimental Demonstration of Acoustic Chern Insulators journal, January 2019

Elastic Higher-Order Topological Insulator with Topologically Protected Corner States journal, May 2019

Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States
journal, March 2011

Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides
journal, May 2011

Left-handed and right-handed one-way edge modes in a gyromagnetic photonic crystal
journal, June 2010

Local density of states of chiral Hall edge states in gyrotropic photonic clusters
journal, July 2013

Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal
journal, March 2010

One-way edge mode in a gyromagnetic photonic crystal slab
journal, January 2012

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
journal, March 2013

Topological States and Adiabatic Pumping in Quasicrystals
journal, September 2012

Photonic Floquet topological insulators
journal, April 2013

Weyl points and line nodes in gyroid photonic crystals
journal, March 2013

Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces
journal, July 2010

Highly efficient photonic-crystal splitters based on one-way waveguiding
journal, December 2012

Microscopic theory of photonic one-way edge mode
journal, August 2011

Robust optical delay lines with topological protection
journal, August 2011

Large-Chern-Number Quantum Anomalous Hall Effect in Thin-Film Topological Crystalline Insulators
journal, January 2014

Realizing effective magnetic field for photons by controlling the phase of dynamic modulation
journal, October 2012

Edge mode in nonreciprocal photonic crystal waveguide: manipulating the unidirectional electromagnetic pulse dynamically
journal, January 2011

Photonic topological insulators
journal, December 2012

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988

Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
journal, June 2005

Effective theory of quadratic degeneracies
journal, June 2008

Quantum Anomalous Hall Effect with Higher Plateaus
journal, September 2013

Experimental demonstration of one-way slow wave in waveguide involving gyromagnetic photonic crystals
journal, June 2013

Chern number and edge states in the integer quantum Hall effect
journal, November 1993

Analogs of quantum-Hall-effect edge states in photonic crystals
journal, September 2008

Observation of unidirectional backscattering-immune topological electromagnetic states
journal, October 2009

One-way edge mode in a magneto-optical honeycomb photonic crystal
journal, July 2009

Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
journal, January 2008

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
journal, January 2008

Broadband circulators based on directional coupling of one-way waveguides
journal, January 2011

Photonic Floquet topological insulators
conference, September 2013

Photonic Topological Insulators
journal, January 2013

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
text, January 2007

Robust optical delay lines via topological protection
text, January 2011

Photonic Floquet Topological Insulators
text, January 2012

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
text, January 2016

Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
text, January 2005

Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
text, January 2005

Applications of Topological Photonics in Integrated Photonic Devices
journal, August 2017

Thermo-optical Tunable Ultracompact Chip-Integrated 1D Photonic Topological Insulator
journal, December 2017

Extremely Broadband Topological Surface States in a Photonic Topological Metamaterial
journal, July 2019

Resonant Transmission through Topological Metamaterial Grating
journal, August 2018

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays: Topological phase transitions and Thouless pumping of light in photonic waveguide arrays
journal, October 2016

Universal numerical calculation method for the Berry curvature and Chern numbers of typical topological photonic crystals
journal, January 2020

Floquet topological insulators for sound
journal, June 2016

Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states
journal, October 2016

Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
journal, December 2014

Topological photonics
journal, October 2014

Synthetic gauge flux and Weyl points in acoustic systems
journal, September 2015

Topological states in photonic systems
journal, June 2016

Topological light-trapping on a dislocation
journal, June 2018

Robust temporal pumping in a magneto-mechanical topological insulator
journal, February 2020

Two-dimensional topological photonics
journal, November 2017

The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry
journal, February 2015

Dirac directional emission in anisotropic zero refractive index photonic crystals
journal, August 2015

Equivalence of electric, magnetic, and electromagnetic Chern numbers for topological photonic crystals
journal, February 2020

Observation of topological edge states of acoustic metamaterials at subwavelength scale
journal, April 2018

Nodal-line semimetal superlattices
journal, November 2018

Topological phase transition with p orbitals in the exciton-polariton honeycomb lattice
journal, June 2019

Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow
journal, May 2015

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale
journal, July 2017

Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology
journal, September 2019

One-way edge modes in truncated semiconductor photonic crystal at terahertz frequencies
journal, May 2019

Ultra-subwavelength focusing and giant magnetic-field enhancement in a low-loss one-way waveguide based on remanence
journal, January 2020

Floquet engineering of exotic topological phases in systems of cold atoms
journal, August 2019

Topological Edge State in the Two-Dimensional Stampfli-Triangle Photonic Crystals
journal, October 2019

Floquet engineering with particle swarm optimization: Maximizing topological invariants
journal, December 2019

Large Chern-number topological superfluids in a coupled-layer system
journal, April 2015

Towards large-Chern-number topological phases by periodic quenching
journal, May 2016

Configurable Dirac-like conical dispersions in complex photonic crystals
journal, January 2017

Topological phases in a Weyl semimetal multilayer
journal, April 2017

Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation
journal, July 2017

Observation of valleylike edge states of sound at a momentum away from the high-symmetry points
journal, April 2018

Recipe for creating an arbitrary number of Floquet chiral edge states
journal, June 2018

Experimental Demonstration of Acoustic Chern Insulators
journal, January 2019

Elastic Higher-Order Topological Insulator with Topologically Protected Corner States
journal, May 2019

Space-time phononic crystals with anomalous topological edge states
journal, November 2019

A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension
journal, October 2018

PT symmetric Floquet topological phase
journal, July 2015

Observation of broadband unidirectional transmission by fusing the one-way edge states of gyromagnetic photonic crystals
journal, January 2015