Gapped topological kink states and topological corner states in honeycomb lattice

Yang, Yuting; Jia, Ziyuan; Wu, Yijia; Xiao, Rui-Chun; Hang, Zhi Hong; Jiang, Hua; Xie, Xin

doi:10.1016/j.scib.2020.01.024

Cited by 81 publications

(28 citation statements)

References 62 publications

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“…A network of narrow channels (also described as "interface solitons") separating the distinct regions with AB and BA alignment develops. It is well known from the study of stacking defects in aligned graphene layers that we find two (pairs of) chiral edge modes at such interfaces, a problem that has been well studied, both theoretically and experimentally [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In twisted bilayer systems such states hybridize with the electronic spectrum in the AB aligned regions, but on applying an electric bias between the two layers, to which the edge states are not sensitive, one should be able to create a gap for the AB states, thus liberating the channel states.…”

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confidence: 89%

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

Walet

Guinea

2019

2D Mater.

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We generalize the continuum model for Moiré structures made from twisted graphene layers, in order to include lattice relaxation and the formation of channels at very small (marginal) twist angles. We show that a precise description of the electronic structure at such small angles can be achieved by i) calculating first the relaxed atomic structure, ii) projecting the interlayer electronic hopping parameters using a suitable basis of Bloch states, and iii) increasing the number of harmonics in the continuum approximation to interlayer hopping. The results show a complex structure of quasi one dimensional states when a finite bias is applied. * Niels.Walet@manchester.ac.uk; http://bit.ly/nielswalet † Francisco.Guinea@imdea.org

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confidence: 89%

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

Walet

Guinea

2019

2D Mater.

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“…The existence of one-dimensional hinge states has been experimentally confirmed in bismuth [60] and multi-layer WTe 2 [61]. In 2D higher-order TIs, one-dimensional edges are insulating whereas the cor-ners between different edges can host zero-dimensional ingap states that are isolated from both edge and bulk bands by an energy gap [53][54][55][62][63][64][65]. In contrast to the gapless edge states in conventional topological insulators, higherorder topological corner states are not conducting and behave like localized bound states.…”

Section: Introductionmentioning

confidence: 93%

Transport induced dimer state from topological corner states

Wang

Ren

et al. 2021

Sci. China Phys. Mech. Astron.

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Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise at the corners with obtuse angles of an isolated diamond-shaped flake. To probe the corner states, we study their transport properties by attaching two leads to the system. Dressed by incoming electrons, the dynamic corner state is very different from its static counterpart. Resonant tunneling through the dressed corner state can occur by tuning the in-plane Zeeman field. At the resonance, the pair of spatially well separated and highly localized corner states can form a dimer state, whose wavefunction extends almost the entire bulk of the diamond-shaped flake. By varying the Zeeman field strength, multiple resonant tunneling events are mediated by the same dimer state. This re-entrance effect can be understood by a simple model. These findings extend our understanding of dynamic aspects of the second-order topological corner states.

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“…When the six cylinders in one unit cell are moved closer to the center of the unit cell, decreasing the intercylinder distance, a shrunken-latticed PCm3 is constructed where its expanded counterpart is considered as PCm4, both shown in gray in Figure 5A. The lattice deformation not only provides an extra mechanism for the bandgap opening of the linear dispersion of two interface states [35], but also leads to the quantum spin Hall effect of photonic crystals [36,37]. With the bandgap of the interfacial state dispersion, PCm3 and PCm4 can serve as the PC mirrors for OTC type II.…”

Section: Optical Topological Cavity Type IImentioning

confidence: 99%

Construction of Optical Topological Cavities Using Photonic Crystals

Meng

Hang

2021

Front. Phys.

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A novel design of the Fabry–Pérot optical cavity is proposed, utilizing both the topological interface state structures and photonic bandgap materials with a controllable reflection phase. A one-to-one correspondence between the traditional Fabry–Pérot cavity and optical topological cavity is found, while the tunable reflection phase of the photonic crystal mirrors provides an extra degree of freedom on cavity mode selection. The relationship between the Zak phase and photonic bandgap provides theoretical guidance to the manipulation of the reflection phase of photonic crystals. The dispersions of interface states with different topology origins are explored. Linear interfacial dispersion emerging in photonic crystals with the valley–spin Hall effect leads to an extra n = 0 cavity mode compared to the Zak phase–induced deterministic interface states with quadratic dispersion. The frequency of the n = 0 cavity mode is not affected by the cavity length, whose quality factor can also be tuned by the thickness of the photonic crystal mirrors. With the recent help of topology photonics in the tuning reflection phase and dispersion relationship, we hope our results can provide more intriguing ideas to construct topological optical devices.

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Gapped topological kink states and topological corner states in honeycomb lattice

Cited by 81 publications

References 62 publications

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

Transport induced dimer state from topological corner states

Construction of Optical Topological Cavities Using Photonic Crystals

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