Higher-order topological phases in a spring-mass model on a breathing kagome lattice

Wakao, Hiromasa; Yoshida, Tsuneya; Araki, Hiromu; Mizoguchi, Tsuyoshi; Hatsugai, Yasuhiro

doi:10.1103/physrevb.101.094107

Cited by 66 publications

(30 citation statements)

References 67 publications

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“…1(k)]. The chain consists of N 1 unit cells with the rotors as well as the fixed pivots labeled A n 1 and B n 1 (1 n 1 N 1 ) and is subjected to fixed boundary conditions [111,112] at rotors B 0 and A N 1 +1 . The equilibrium configuration is that the A rotors (B rotors) make an (1,15) with ω ext = 1.13 and F = 10 −10 .…”

Section: A Non-hermitian Topological Mechanics In the 1d Rotor Chainmentioning

confidence: 99%

Non-Hermitian topological metamaterials with odd elasticity

Zhou

Zhang

2020

Phys. Rev. Research

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We establish non-Hermitian topological mechanics in one-dimensional (1D) and 2D lattices consisting of mass points connected by metabeams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of PT symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems.

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Section: A Non-hermitian Topological Mechanics In the 1d Rotor Chainmentioning

confidence: 99%

Non-Hermitian topological metamaterials with odd elasticity

Zhou

Zhang

2020

Phys. Rev. Research

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“…We have demonstrated a conceptually new on-surface synthesis route towards the ultra-high anomalous quantum Hall states [42][43][44] , Wigner crystallization [45] and topological insulating transitions [46] .…”

Section: Discussionmentioning

confidence: 99%

Ultra-high Yield On-surface Synthesis and Assembly of Circumcoronene into Chiral Electronic Kagome-honeycomb Lattice

Telychko

Li²,

Mutombo³

et al. 2020

Preprint

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On-surface synthesis has revealed remarkable potential in the fabrication of a plethora of elusive nanographenes with tailored structural, electronic and magnetic properties unattainable by conventional wet-chemistry synthesis. Unfortunately, surface-assisted synthesis often involves multiple-step cascade reactions with competing pathways, leading to the formation of a diversity of products with limited yield, which reduces its feasibility towards the large-scale production for future technological applications. Here, we devise a new on-surface synthetic strategy for the ultra-high yield synthesis of a hexagonal nanographene with six zigzag edges, namely circumcoronene on Cu(111) via surfaceassisted intramolecular dehydrogenation of the rationally-designed precursor molecule, followed by methyl radical-radical coupling and aromatization. An elegant electrostatic interaction between circumcoronene and Cu(111) drives their self-organization into an extended superlattice, as revealed by bond-resolved low-temperature scanning probe microscopy and spectroscopy measurements. Density functional theory and tight-binding calculations reveal that unique hexagonal zigzag topology of circumcoronenes, along with their periodic electrostatic landscape confines two-dimensional (2D) electron gas in Cu(111) surface into chiral electronic Kagome-honeycomb lattice with two emergent electronic flat bands. Our findings open up a new route for the high-yield fabrication of elusive nanographenes with zigzag topologies and their novel 2D superlattices with possible nontrivial electronic properties towards their future technological applications.

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“…For example, 2D second-order topological phases have not only 1D edge states but also 0D corner states, [27,28] promising the realization of nanoscale cavities. [9,11] Various invariants, such as the quadrupole moment, [29][30][31][32] Z N Berry phase, [33][34][35] mirror Chern number, [36] nested Wilson loops and polarization, [25,37,38] have been suggested to characterize these new phases. In parallel with these theoretical studies, the higher-order topological phases have been experimentally observed in quantum [39] and classical systems, including microwave circuits, [40] topolectric circuits, [41] acoustic, [42][43][44][45] and photonic systems, [28,[46][47][48] respectively.…”

Section: Introductionmentioning

confidence: 99%

Corner States in 2D Square Lattice Second‐Order Photonic Topological Insulators Composed of L‐Shaped Sublattices

Kim

2021

Physica Status Solidi (b)

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Higher‐order photonic topological states have recently attracted great attention due to the realizability of photonic nanocavities with high robustness against structural disorder. Herein, it is revealed that square‐lattice photonic crystals with L‐shaped sublattices exhibit second‐order photonic topological phases. In the approximation considering only the nearest‐neighbor interactions, the photonic system with an expanded sublattice exhibits topologically nontrivial phase represented by the nonzero polarization, approaching P = ( 1 4 , 1 4 ) in the extreme case, whereas it is trivial for the cases of the shrunken one. Unlike the conventional square lattices with four dielectric rods, the proposed photonic systems have a single corner state for squared topological boundaries, while they exhibit three corner states when they have triangular boundaries. Although the weakly anisotropic systems with the expanded L‐shaped sublattices exhibit different corner states, they disappear for a substantial increase of anisotropy. The results obtained in this work enrich the diversity and understanding of higher‐order photonic topological systems and pave the way for wide applications of higher‐order topological phases in photonics, including coherent nanosources based on nanolasing and nonlinear frequency conversion.

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Higher-order topological phases in a spring-mass model on a breathing kagome lattice

Cited by 66 publications

References 67 publications

Non-Hermitian topological metamaterials with odd elasticity

Non-Hermitian topological metamaterials with odd elasticity

Ultra-high Yield On-surface Synthesis and Assembly of Circumcoronene into Chiral Electronic Kagome-honeycomb Lattice

Corner States in 2D Square Lattice Second‐Order Photonic Topological Insulators Composed of L‐Shaped Sublattices

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