Topological modes in one-dimensional solids and photonic crystals

Atherton, Timothy J.; Butler, Celia A. M.; Taylor, Melita C.; Hooper, Ian R.; Hibbins, Alastair P.; Sambles, J. R.; Mathur, Harsh

doi:10.1103/physrevb.93.125106

Cited by 7 publications

(5 citation statements)

References 28 publications

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“…We show that the DFT calculations can be explained by a minimal tight-binding (TB) model, closely related to the quadripartite Su-Schrieffer-Heeger (SSH4) model which has been shown to support topologically protected surface states for specific conditions on the interatomic hopping integrals. [8] We further prove this modelindependently in Appendix B by evaluating the inversion operator eigenvalues at time-reversalinvariant momenta (TRIM) in the layer direction. [9] This symmetry indicator is also related to Zak's criterion for Maue-Shockley states.…”

Section: Introductionmentioning

confidence: 71%

“…Ordering the orbitals as {|Li a 〉 , CoO a 2 , Li b , CoO b 2 } the Hamiltonian for the above 1D system (with distance between the layers set to 1) is represented by the following 4 × 4 matrix: to O-Co-O hopping within the layer. This model, which is the SSH4 model for δ = 0 corresponding to chiral symmetry, has been shown [8] to have non-trivial topology which requires zero-energy edge states when…”

Section: Tight-binding Model and Topologymentioning

confidence: 99%

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Spin-polarized two-dimensional electron/hole gases on LiCoO$_2$ layers.

Radha

Lambrecht

2021

SciPost Phys.

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First-principles calculations show the formation of a 2D spin polarized electron (hole) gas on the Li (CoO_22) terminated surfaces of finite slabs down to a monolayer, in remarkable contrast with the bulk band structure, which is stabilized by Li donating its electron to the CoO_22 layer forming a Co-d-t_{2g}^6d−t2g6 insulator. By mapping the first-principles computational results to a minimal tight-binding models corresponding to a non-chiral 3D generalization of the quadripartite Su-Schrieffer-Heeger (SSH4) model and symmetry analysis, we show that these surface states have topological origin.

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Section: Introductionmentioning

confidence: 71%

Section: Tight-binding Model and Topologymentioning

confidence: 99%

Spin-polarized two-dimensional electron/hole gases on LiCoO$_2$ layers.

Radha

Lambrecht

2021

SciPost Phys.

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“…[ 35 , 36 ] This lineshape is ubiquitous from various photonic phenomenon, such as electromagnetically induced transparency, [ 37 ] parity‐time symmetry breaking, [ 38 ] quasi‐bound states in the continuum, [ 39 , 40 ] and topological edge state. [ 41 , 42 ] The steep dispersion of the Fano resonance profile, [ 43 , 44 ] in contrast to standard symmetric resonating curves, promises a variety of applications in sensors, [ 45 , 46 ] lasing, [ 47 , 48 ] switching, nonlinear, [ 49 ] and slow‐light devices. [ 50 , 51 ] These unique features naturally motivate further investigations on ultracompact terahertz modulators.…”

Section: Introductionmentioning

confidence: 99%

Reassessing Fano Resonance for Broadband, High‐Efficiency, and Ultrafast Terahertz Wave Switching

Tong

et al. 2022

Advanced Science

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Miniaturized ultrafast switchable optical components with high efficiency and broadband response are in high demand to the development of optical imaging, sensing, and high‐speed communication. Sharp Fano‐type resonance switched by active materials is one of the key concepts that underpins the control of light in metaoptics with high sensitivity. However, actuating such metasurfaces exhibits a long‐standing trade‐off between modulation depth and operational bandwidth. Here, the limitations are circumvented by theoretical analysis, numerical simulation, and experimental realization of an achromatic Fano metasurface so that a high contrast of tunability with ultrafast switching rate over a broad range of frequency is achieved. By developing the physics of inter‐mode coupling, the Fano metasurface is designed according to a complete phase diagram derived from coupled mode theory. Unlike conventional Fano metasurfaces, the cross‐polarized inter‐metaatoms coupling is discovered as a superior ability of high‐efficiency broadband achromatic polarization conversion. To prove the ultrasensitive nature, a metadevice is constructed by incorporating a thin amorphous Ge layer with a weak photoconductivity perturbation. Transmission modulation over broadband frequency range from 0.6 to 1.1 THz is thus successfully realized, featuring its merits of modulation depth over 90% and On–Off–On switching cycle less than 10 ps.

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“…Topological models in one dimension [5][6][7][8][9][10][11][12][13][14] are also actively studied. Of the many such models, most relevant to our study is the Creutz model [7,8] which exhibits a topological interference effect which can be probed when open boundary conditions are applied (edge-states).…”

Section: Introductionmentioning

confidence: 99%

Extended Creutz ladder with spin-orbit coupling: A one-dimensional analog of the Kane-Mele model

Gholizadeh¹,

Yahyavi²,

Hetényi³

2018

EPL

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We construct a topological ladder model, one-dimensional, following the steps which lead to the Kane-Mele model in two dimensions. Starting with a Creutz ladder we modify it so that the gap closure points can occur at either k = π/2 or −π/2. We then couple two such models, one for each spin channel, in such a way that time-reversal invariance is restored. We also add a Rashba spin-orbit coupling term. The model falls in the CII symmetry class. We derive the relevant 2Z topological index, calculate the phase diagram and demonstrate the existence of edge states. We also give the thermodynamic derivation of the quantum spin Hall conductance (Středa-Widom). Approximate implementation of this result indicates that this quantity is sensitive to the topological behavior of the model.

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Topological modes in one-dimensional solids and photonic crystals

Cited by 7 publications

References 28 publications

Spin-polarized two-dimensional electron/hole gases on LiCoO$_2$ layers.

Spin-polarized two-dimensional electron/hole gases on LiCoO$_2$ layers.

Reassessing Fano Resonance for Broadband, High‐Efficiency, and Ultrafast Terahertz Wave Switching

Extended Creutz ladder with spin-orbit coupling: A one-dimensional analog of the Kane-Mele model

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