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 with 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.

Searching for kagome multi-bands and edge states in a predicted organic topological insulator

“…In essence, our toy model qualitatively demonstrates that this symmetry breaking removes the edge states from the MHK lattice, which disrupts its OTI condition. 53 Unlike this studied network, the free-standing 2D-MOFs theoretically proposed always preserve some mirror and inversion symmetries that lead to preservation of their topological properties, despite being buckled or twisted 8,54,55 or in different forms and shapes. 56,57 Note, however, that the total absence of symmetry does not "per se" leads to the closing of the multi-band gaps since our toy model calculations show that topological conditions are still achievable by increasing the λ/t ratio in reduced symmetry scenarios (see Fig.…”

Nonlinear compact localized modes in flux-dressed octagonal-diamond photonic lattice

“…The first one touches the embedded DB at the boundaries of the BZ, and the second one touches the same DB at the center of BZ [20]. Corresponding band crossings are conical and parabolic, respectively, similar to the Lieb [38,39] and Kagome lattices [38]. Therefore both FBs are singular with singularities in the crossing points with the DB.…”

Recent Progress on 2D Kagome Magnets: Binary TmSnn (T = Fe, Co, Mn)

“…Interestingly, FBs appear topologically non‐trivial in subject to local magnetic field or strong spin‐orbital coupling (SOC), under strict symmetry and coupling requirements. [ 14 ]…”

“…Interestingly, FBs appear topologically non-trivial in subject to local magnetic field or strong spin-orbital coupling (SOC), under strict symmetry and coupling requirements. [14] The 2D kagome [15] and 2D Lieb lattices [16] are the most typical frustrated lattices satisfying the aforementioned criteria for topological non-trivial electronic FBs. The kagome lattice (named after a Japanese basket pattern), reviewed in this article was coined by the Japanese physicist Kôdi Husimi in 1951.…”