Topological band evolution between Lieb and kagome lattices

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

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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

Bibliographical note

Funding Information:
This project is supported by U.S. DOE-BES (Grant No. DE-FG02-04ER46148). W.J. and T.L. acknowledge support in part by SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by National Institute of Standards and Technology (NIST). W.J. is additionally supported by the NSF-Material Research Science & Engineering Center (Grant No. DMR-1121252). M.K. and H.X. thank the financial support from the National Key Basic Research Program (Grant No. 2015CB932400) and the National Natural Science Foundation of China (Grant No. 11674256). M.K. acknowledges Wuhan University which supported him to visit University of Utah and participate in this project. We thank the CHPC at the University of Utah and DOE-NERSC for providing the computing resources.

Funding Information:
W.J. is additionally supported by the NSF-Material Research Science & Engineering Center (Grant No. DMR-1121252). M.K. and H.X. thank the financial support from the National Key Basic Research Program (Grant No. 2015CB932400) and the National Natural Science Foundation of China (Grant No. 11674256). M.K. acknowledges Wuhan University which supported him to visit University of Utah and participate in this project. We thank the CHPC at the University of Utah and DOE-NERSC for providing the computing resources.

Publisher Copyright:
© 2019 American Physical Society.

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