Topological band evolution between Lieb and kagome lattices

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

doi:10.1103/PhysRevB.99.125131

Topological band evolution between Lieb and kagome lattices

Journal Article · Mon Mar 18 00:00:00 EDT 2019 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.99.125131· OSTI ID:1530400

Jiang, Wei ^[1]; Kang, Meng ^[2]; Huang, Huaqing ^[3]; Xu, Hongxing ^[4]; Low, Tony ^[5]; Liu, Feng ^[3]

Univ. of Utah, Salt Lake City, UT (United States). Dept. of Materials Science & Engineering; Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Electrical and Computer Engineering
Wuhan Univ. (China). School of Physics and Technology, Center for Nanoscience and Nanotechnology, Key Lab. of Artificial Micro- and Nano-Structures of Ministry of Education
Univ. of Utah, Salt Lake City, UT (United States). Dept. of Materials Science & Engineering
Wuhan Univ. (China). School of Physics and Technology, Center for Nanoscience and Nanotechnology, Key Lab. of Artificial Micro- and Nano-Structures of Ministry of Education; Wuhan Univ., Wuhan (China). Inst. for Advanced Studies
Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Electrical and Computer Engineering

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. Here, 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

Sponsoring Organization:: National Key Basic Research Program; National Institute of Standards and Technology (NIST); National Natural Science Foundation of China (NSFC); National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-04ER46148

OSTI ID:: 1530400

Alternate ID(s):: OSTI ID: 1501704

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 12 Vol. 99; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Hidden mechanism for embedding the flat bands of Lieb, kagome, and checkerboard lattices in other structures Lee, Chi-Cheng; Fleurence, Antoine; Yamada-Takamura, Yukiko Physical Review B, Vol. 100, Issue 4 https://doi.org/10.1103/physrevb.100.045150	journal	July 2019
Flat bands and nontrivial topological properties in an extended Lieb lattice Bhattacharya, Ankita; Pal, Biplab Physical Review B, Vol. 100, Issue 23 https://doi.org/10.1103/physrevb.100.235145	journal	December 2019
Kagome bands disguised in a coloring-triangle lattice Zhang, Shunhong; Kang, Meng; Huang, Huaqing Physical Review B, Vol. 99, Issue 10 https://doi.org/10.1103/physrevb.99.100404	journal	March 2019
Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices Lima, F. Crasto De; Ferreira, Gerson J.; Miwa, R. H. Unpublished https://doi.org/10.13140/rg.2.2.32912.35849	text	January 2019

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