Topological band evolution between Lieb and kagome lattices

Wei Jiang, Meng Kang, Huaqing Huang, Hongxing Xu, Tony Low, Feng Liu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Among two-dimensional lattices, both kagome and Lieb lattices have been extensively studied, showing unique physics related to their exotic flat and Dirac bands. Interestingly, we realize that the two lattices are in fact interconvertible by applying strains along the diagonal direction, as they share the same structural configuration in the unit cell, i.e., one corner-site and two edge-center states. We study phase transitions between the two lattices using the tight-binding approach and propose one experimental realization of the transitions using photonic devices. The evolution of the band structure demonstrates a continuous evolution of the flat band from the middle of the Lieb band to the top/bottom of the kagome band. Though the flat band is destroyed during the transition, the topological features are conserved due to the retained inversion symmetry, as confirmed by Berry curvature, Wannier charge center, and edge state calculations. Meanwhile, the triply degenerate Dirac point (M) in the Lieb lattice transforms into two doubly degenerate Dirac points, one of which moves along M-Γ and the other moves along M-K/K′ directions that form the kagome band eventually. Interestingly, the Dirac cones in the transition states are strongly tilted, showing a coexistence of type-I and type-II Dirac points. We finally show that these transitions can be experimentally realized in photonic lattices using waveguide arrays.

Original languageEnglish (US)
Article number125131
JournalPhysical Review B
Volume99
Issue number12
DOIs
StatePublished - Mar 18 2019

Fingerprint

Optical lattices
Photonic devices
Band structure
Cones
Waveguides
Physics
Phase transitions
photonics
Direction compound
cones
curvature
inversions
waveguides
physics
symmetry
configurations
cells

Cite this

Topological band evolution between Lieb and kagome lattices. / Jiang, Wei; Kang, Meng; Huang, Huaqing; Xu, Hongxing; Low, Tony; Liu, Feng.

In: Physical Review B, Vol. 99, No. 12, 125131, 18.03.2019.

Research output: Contribution to journalArticle

Jiang, Wei ; Kang, Meng ; Huang, Huaqing ; Xu, Hongxing ; Low, Tony ; Liu, Feng. / Topological band evolution between Lieb and kagome lattices. In: Physical Review B. 2019 ; Vol. 99, No. 12.
@article{3add7f1c416c4c56bec1f7d35b700b16,
title = "Topological band evolution between Lieb and kagome lattices",
abstract = "Among two-dimensional lattices, both kagome and Lieb lattices have been extensively studied, showing unique physics related to their exotic flat and Dirac bands. Interestingly, we realize that the two lattices are in fact interconvertible by applying strains along the diagonal direction, as they share the same structural configuration in the unit cell, i.e., one corner-site and two edge-center states. We study phase transitions between the two lattices using the tight-binding approach and propose one experimental realization of the transitions using photonic devices. The evolution of the band structure demonstrates a continuous evolution of the flat band from the middle of the Lieb band to the top/bottom of the kagome band. Though the flat band is destroyed during the transition, the topological features are conserved due to the retained inversion symmetry, as confirmed by Berry curvature, Wannier charge center, and edge state calculations. Meanwhile, the triply degenerate Dirac point (M) in the Lieb lattice transforms into two doubly degenerate Dirac points, one of which moves along M-Γ and the other moves along M-K/K′ directions that form the kagome band eventually. Interestingly, the Dirac cones in the transition states are strongly tilted, showing a coexistence of type-I and type-II Dirac points. We finally show that these transitions can be experimentally realized in photonic lattices using waveguide arrays.",
author = "Wei Jiang and Meng Kang and Huaqing Huang and Hongxing Xu and Tony Low and Feng Liu",
year = "2019",
month = "3",
day = "18",
doi = "10.1103/PhysRevB.99.125131",
language = "English (US)",
volume = "99",
journal = "Physical Review B",
issn = "2469-9950",
number = "12",

}

TY - JOUR

T1 - Topological band evolution between Lieb and kagome lattices

AU - Jiang, Wei

AU - Kang, Meng

AU - Huang, Huaqing

AU - Xu, Hongxing

AU - Low, Tony

AU - Liu, Feng

PY - 2019/3/18

Y1 - 2019/3/18

N2 - Among two-dimensional lattices, both kagome and Lieb lattices have been extensively studied, showing unique physics related to their exotic flat and Dirac bands. Interestingly, we realize that the two lattices are in fact interconvertible by applying strains along the diagonal direction, as they share the same structural configuration in the unit cell, i.e., one corner-site and two edge-center states. We study phase transitions between the two lattices using the tight-binding approach and propose one experimental realization of the transitions using photonic devices. The evolution of the band structure demonstrates a continuous evolution of the flat band from the middle of the Lieb band to the top/bottom of the kagome band. Though the flat band is destroyed during the transition, the topological features are conserved due to the retained inversion symmetry, as confirmed by Berry curvature, Wannier charge center, and edge state calculations. Meanwhile, the triply degenerate Dirac point (M) in the Lieb lattice transforms into two doubly degenerate Dirac points, one of which moves along M-Γ and the other moves along M-K/K′ directions that form the kagome band eventually. Interestingly, the Dirac cones in the transition states are strongly tilted, showing a coexistence of type-I and type-II Dirac points. We finally show that these transitions can be experimentally realized in photonic lattices using waveguide arrays.

AB - Among two-dimensional lattices, both kagome and Lieb lattices have been extensively studied, showing unique physics related to their exotic flat and Dirac bands. Interestingly, we realize that the two lattices are in fact interconvertible by applying strains along the diagonal direction, as they share the same structural configuration in the unit cell, i.e., one corner-site and two edge-center states. We study phase transitions between the two lattices using the tight-binding approach and propose one experimental realization of the transitions using photonic devices. The evolution of the band structure demonstrates a continuous evolution of the flat band from the middle of the Lieb band to the top/bottom of the kagome band. Though the flat band is destroyed during the transition, the topological features are conserved due to the retained inversion symmetry, as confirmed by Berry curvature, Wannier charge center, and edge state calculations. Meanwhile, the triply degenerate Dirac point (M) in the Lieb lattice transforms into two doubly degenerate Dirac points, one of which moves along M-Γ and the other moves along M-K/K′ directions that form the kagome band eventually. Interestingly, the Dirac cones in the transition states are strongly tilted, showing a coexistence of type-I and type-II Dirac points. We finally show that these transitions can be experimentally realized in photonic lattices using waveguide arrays.

UR - http://www.scopus.com/inward/record.url?scp=85063223561&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063223561&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.99.125131

DO - 10.1103/PhysRevB.99.125131

M3 - Article

VL - 99

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 12

M1 - 125131

ER -