Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Quadrupole topological photonic crystals

Abstract

Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell’s equations for a gyromagnetic photonic crystal (PhC) through a double-band-inversion process. The quadrupole moment is quantized by the simultaneous presence of crystalline symmetry and broken time-reversal symmetry, which is confirmed using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands and the expectation value of the quadrupole operator. Furthermore, we reveal the boundary manifestations of quadrupole phases as quantized edge polarizations and fractional corner charges. The latter are the consequence of a filling anomaly of energy bands as first predicted in electronic systems.

Authors:
 [1];  [1];  [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); US Air Force Office of Scientific Research (AFOSR); Army Research Office (ARO)
OSTI Identifier:
1647001
Grant/Contract Number:  
FG02-84ER45118; DMR-1720530; N00014-20-1-2325; FA9550-18-1-0133; W911NF-19-1-0087
Resource Type:
Accepted Manuscript
Journal Name:
Nature Communications
Additional Journal Information:
Journal Volume: 11; Journal Issue: 1; Journal ID: ISSN 2041-1723
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optical physics; Photonic crystals

Citation Formats

He, Li, Addison, Zachariah, Mele, Eugene J., and Zhen, Bo. Quadrupole topological photonic crystals. United States: N. p., 2020. Web. doi:10.1038/s41467-020-16916-z.
Copy to clipboard
He, Li, Addison, Zachariah, Mele, Eugene J., & Zhen, Bo. Quadrupole topological photonic crystals. United States. https://doi.org/10.1038/s41467-020-16916-z
Copy to clipboard
He, Li, Addison, Zachariah, Mele, Eugene J., and Zhen, Bo. Fri . "Quadrupole topological photonic crystals". United States. https://doi.org/10.1038/s41467-020-16916-z. https://www.osti.gov/servlets/purl/1647001.
Copy to clipboard
@article{osti_1647001,
title = {Quadrupole topological photonic crystals},
author = {He, Li and Addison, Zachariah and Mele, Eugene J. and Zhen, Bo},
abstractNote = {Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell’s equations for a gyromagnetic photonic crystal (PhC) through a double-band-inversion process. The quadrupole moment is quantized by the simultaneous presence of crystalline symmetry and broken time-reversal symmetry, which is confirmed using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands and the expectation value of the quadrupole operator. Furthermore, we reveal the boundary manifestations of quadrupole phases as quantized edge polarizations and fractional corner charges. The latter are the consequence of a filling anomaly of energy bands as first predicted in electronic systems.},
doi = {10.1038/s41467-020-16916-z},
journal = {Nature Communications},
number = 1,
volume = 11,
place = {United States},
year = {Fri Jun 19 00:00:00 EDT 2020},
month = {Fri Jun 19 00:00:00 EDT 2020}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1038/s41467-020-16916-z
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 53 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Quadrupole topological phase transitions through super-cell PhCs. a Band degeneracies are created at the center (Γ) and corner (M) of the folded Brilluion zone for a 2 x 2 super-cell PhC (inset). An external magnetic field (B) induces gyromagnetic responses in YIG rods (gray squares), which breaks Tmore » but preserves C4. The gyromagnetic response κ= 12.4μ0 is used in the calculations. b, c As the rods simultaneously move inward or outward, the second gap is opened (shaded in yellow), but with different quadrupole phases: inward (outward) displacements with negative (positive) d correspond to trivial (non-trivial) quadrupole phases. d, e Ez mode profiles for the second and third modes at M feature a band inversion between the modes with C4 index of +i (green) and −i (red) in the trivial and non-trivial phases. f Complete topological phase diagram of the PhCs, including quadrupole phases (green), trivial phases (orange), and Chern insulating phases (purple). Systems are gapless along the axes (red). NI normal insulator, QTI quadrupole insulator, CI Chern insulator.« less
All figures and tables (4 total)
Save / Share:
Export Metadata
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:

Observation of a phononic quadrupole topological insulator
journal, January 2018

  • Serra-Garcia, Marc; Peri, Valerio; Süsstrunk, Roman
  • Nature, Vol. 555, Issue 7696
  • DOI: 10.1038/nature25156

Experimental Observation of Large Chern Numbers in Photonic Crystals
journal, December 2015

Higher-order topological insulators
journal, June 2018

  • Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
  • Science Advances, Vol. 4, Issue 6
  • DOI: 10.1126/sciadv.aat0346

Multimode One-Way Waveguides of Large Chern Numbers
journal, September 2014

Berry’s phase for energy bands in solids
journal, June 1989

Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators
journal, December 2017

  • Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.
  • Physical Review B, Vol. 96, Issue 24
  • DOI: 10.1103/PhysRevB.96.245115

Corner states of light in photonic waveguides
journal, September 2019

Observation of quadrupole transitions and edge mode topology in an LC circuit network
journal, January 2019

Classification of topological insulators and superconductors in three spatial dimensions
journal, November 2008

Second-order topology and multidimensional topological transitions in sonic crystals
journal, March 2019

Reflection-Symmetric Second-Order Topological Insulators and Superconductors
journal, December 2017

( d − 2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States
journal, December 2017

Topolectrical-circuit realization of topological corner modes
journal, September 2018

Quantization of fractional corner charge in C n -symmetric higher-order topological crystalline insulators
journal, June 2019

Topological protection of photonic mid-gap defect modes
journal, June 2018

Classification of topological quantum matter with symmetries
journal, August 2016

Many-body order parameters for multipoles in solids
journal, December 2019

Periodic table for topological insulators and superconductors
conference, January 2009

  • Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
  • ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
  • DOI: 10.1063/1.3149495

Quantized electric multipole insulators
journal, July 2017

  • Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.
  • Science, Vol. 357, Issue 6346
  • DOI: 10.1126/science.aah6442

Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs
journal, June 2019

Observation of higher-order topological acoustic states protected by generalized chiral symmetry
journal, December 2018

Acoustic higher-order topological insulator on a kagome lattice
journal, December 2018

Many-body electric multipole operators in extended systems
journal, December 2019

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

  • Wang, Zheng; Chong, Yidong; Joannopoulos, J. D.
  • Nature, Vol. 461, Issue 7265
  • DOI: 10.1038/nature08293

A quantized microwave quadrupole insulator with topologically protected corner states
journal, March 2018

  • Peterson, Christopher W.; Benalcazar, Wladimir A.; Hughes, Taylor L.
  • Nature, Vol. 555, Issue 7696
  • DOI: 10.1038/nature25777

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

Second-order photonic topological insulator with corner states
journal, November 2018

Strong and fragile topological Dirac semimetals with higher-order Fermi arcs
journal, January 2020

Photonic quadrupole topological phases
journal, June 2019

Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010

    Sort by:
    [ × clear filter / sort ]

    Figures / Tables found in this record:

    Fig. 1 (p. 3)figure
    Fig. 2 (p. 3)figure
    Fig. 3 (p. 4)figure
    Fig. 4 (p. 5)figure
      [ × clear filter / sort ]
      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

      Similar Records in DOE PAGES and OSTI.GOV collections: